3‐D Ionospheric Imaging Over the South American Region With a New TEC‐Based Ionospheric Data Assimilation System (TIDAS‐SA)

This study has developed a new TEC‐based ionospheric data assimilation system for 3‐D regional ionospheric imaging over the South American sector (TIDAS‐SA) (45°S–15°N, 35°–85°W, and 100–800 km). The TIDAS‐SA data assimilation system utilizes a hybrid Ensemble‐Variational approach to incorporate a diverse set of ionospheric data sources, including dense ground‐based Global Navigation Satellite System (GNSS) line‐of‐sight Total Electron Content (TEC) data, radio occultation data from the Constellation Observing System for Meteorology, Ionosphere, and Climate‐2 (COSMIC‐2), and altimeter TEC data from the JASON‐3 satellite. TIDAS‐SA can produce a reanalyzed three‐dimensional (3‐D) electron density spatial variation with a high time cadence, yielding spatial‐temporal resolution of 1° (latitude) × 1° (longitude) × 20 km (altitude) × 5 min. This allows us to reconstruct and study the 3‐D ionospheric morphology with multi‐scale structures. The performance of the data assimilation system is validated against independent ionosonde and in situ measurements through an experiment for a strong geomagnetic storm event on 03–04 November 2021. The results demonstrate that TIDAS‐SA can provide detailed and altitude‐resolved information that accurately characterizes the storm‐time ionospheric disturbances in vertical and horizontal domains over the equatorial and low‐latitude regions of South America.

particularly in the three-dimensional (3-D) domain, has taken rather high profiles within both scientific and engineering communities (Aa, Forsythe, et al., 2023).
The data assimilation technique has gained widespread use in ionospheric imaging, where various measurements are integrated into a background model to achieve a more accurate state estimation for the specific region of interest.Several common optimization techniques for data assimilation are available, including recursive estimation methods like the Kalman filter and its various derivatives (Evensen, 1994;Kalman, 1960), as well as typical variational approaches such as 3-D/4-D variational algorithms (Barker et al., 2004).Previously, a considerable number of pioneering ionospheric data assimilation models have been established, such as the Assimilative Mapping of Ionospheric Electrodynamics (AMIE) (Richmond, 1992), the Global Assimilation of Ionospheric Measurements developed by Utah State University (USU-GAIM) (Scherliess et al., 2006;Schunk et al., 2004), and the Global Assimilative Ionospheric Model built by Jet Propulsion Laboratory and the University of Southern California and (USC/JPL-GAIM) (Komjathy et al., 2010;C. Wang et al., 2004).In recent decades, substantial efforts have been devoted towards obtaining a more accurate specification of the ionospheric state, utilizing data assimilation techniques based on coupled ionosphere-thermosphere models.Examples including the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM, Richmond et al., 1992) and the Whole Atmosphere Community Climate Model with thermosphere ionosphere eXtension (WACCM-X, H.-L. Liu et al., 2018) as implemented via the Data Assimilation Research Testbed (DART, Anderson et al., 2009), as well as the coupled Whole Atmosphere Model-Ionosphere Plasmasphere Electrodynamics (WAM-IPE, Akmaev, 2011;Maruyama et al., 2016) data assimilation system using the Gridpoint Statistical Interpolation software (H.Wang et al., 2011).Despite the current high computation cost, these data assimilation systems on the basis of theoretical models have the advantage of providing physics-based ionospheric forecasts with longer timescales due to the self-consistent thermosphere-ionosphere coupling condition, which have been widely used to gain a better understanding of ionospheric/thermospheric variability (e.g., Chartier et al., 2016;Chen et al., 2016;Fang et al., 2016;He et al., 2019;Hsu et al., 2018;Lee et al., 2012;Matsuo & Araujo-Pradere, 2011;Pedatella et al., 2020).
Furthermore, empirical ionospheric models, such as the International Reference Ionosphere (IRI, Bilitza, 2001;Bilitza et al., 2017) and the NeQuick model (Nava et al., 2008;Radicella, 2009), have also been extensively employed in the development of ionospheric data assimilation systems.Examples include the Ionospheric Data Assimilation Three/Four-Dimensional (IDA3D/4D) (Bust et al., 2004(Bust et al., , 2007)), the Global Ionospheric Specification (GIS) (Lin et al., 2015(Lin et al., , 2017)), the United States/North American TEC (Fuller-Rowell et al., 2006;Spencer et al., 2004), the Multi-Instrument Data Analysis System (MIDAS) (Mitchell & Spencer, 2003;Spencer & Mitchell, 2007), as well as various global/regional ionospheric data assimilation systems driven by multiple data sources (e.g., Aa et al., 2018Aa et al., , 2022;;Forsythe et al., 2020Forsythe et al., , 2021;;Galkin et al., 2012;Mengist et al., 2019;Reid et al., 2023;Ssessanga et al., 2019;H. Wu et al., 2022;Yue et al., 2012Yue et al., , 2014)).The empirical model-based data assimilation system has the merits of low computational cost and can be used for ionospheric imaging with potential near-real-time capabilities, although it could be somewhat limited by the issue of under-performance in regions with scarce data.Therefore, the varied array of ionospheric data assimilation models, each with their own distinct strengths and challenges, as well as strategies for surmounting their constraints, persistently motivates the space weather community to advance data assimilation techniques and to improve ionospheric imaging capabilities.
Significant advancements have been accomplished in the field of ionospheric imaging and data assimilation studies over the preceding decades.However, certain noteworthy challenges continue to persist, demanding additional focus and effort from the scientific community.These include: 1. High-fidelity ionospheric imaging in the 3-D domain.Integrated TEC measurements derived from ground-based GNSS receivers stand as the predominant data set for ionospheric imaging, which can be directly employed to generate 2-D imaging maps of the ionosphere, providing detailed information about horizontal features of ionospheric morphology (e.g., Fuller-Rowell et al., 2006;Hernández-Pajares et al., 2009;Mannucci et al., 1998).Nevertheless, crucial details regarding ionospheric vertical structures would be missing in the 2-D imaging, and the altitudinal variation of the ionosphere is quite important in providing unique information on ionospheric thermal configuration and dynamics, such as vertical plasma motion and scale height (Aa, Forsythe, et al., 2023).Furthermore, the electron density distribution is actually the most significant parameter that lends considerable utility to ionospheric imaging from the application standpoint, as it imposes various ionospheric effects on radio signals.Thus, the accurate 3-D spatial distribution and 1-D temporal evolution (i.e., 4-D) of the electron density is the foremost requirement for ionospheric imaging and radio system applications.Through a high-fidelity 3-D ionospheric imaging, our understanding of the multi-scale ionospheric plasma structures can be further advanced.Recently, certain studies have effectively carried out 3-D ionospheric imaging to investigate ionospheric variability and weather disturbances (Aa, Zhang, Erickson, et al., 2023;Aa et al., 2022;Datta-Barua et al., 2011;Forsythe et al., 2021;Lin et al., 2017;Prol et al., 2021;Zhai et al., 2020).2. Developing high-resolution regional ionospheric data assimilation system for key areas of focus.Several existing ionospheric data assimilation systems have been developed to operate on a global scale using a relatively coarse grid (e.g., 2.5° lat × 5° lon), which somewhat limits their capacity to accurately characterize localized ionospheric features in great detail for specific regions of interest.Over the years, some dedicated regional ionospheric data assimilation models and/or imaging systems have been designed for certain regions, such as North American sector (e.g., Aa et al., 2022;Forsythe et al., 2021;Fuller-Rowell et al., 2006;Zhai et al., 2020), East Asian sector (e.g., Aa et al., 2015Aa et al., , 2016;;Jeong et al., 2022;Mengist et al., 2019), European sector (e.g., Dear & Mitchell, 2006;Jakowski et al., 2011;L. Liu et al., 2019), and African sector (e.g., Chartier et al., 2014;Habarulema & Ssessanga, 2017;Mengist et al., 2023;Ssessanga et al., 2019).In particular, the low-latitude and equatorial ionosphere over the South American longitude sector has consistently attracted significant space weather research attention with growing scientific interest, since this region is characterized by strong plasma density gradients such as the dynamic variation of equatorial ionization anomaly (EIA), where the geomagnetic dip equator exhibits the largest offset with respect to geographic equator also with large declination angles, resulting in complicated dynamics and electrodynamics.While many pioneering efforts have been undertaken to image the ionosphere in this region by using measurements from dense networks of ground-based GNSS receivers (e.g., Muella et al., 2011;Takahashi et al., 2016;Zapfe et al., 2006), these studies have primarily concentrated on either 2-D TEC mapping or imaging a specific portion of the EIA crest within a smaller area.Hence, there still remains a pressing need to develop a comprehensive 3-D regional ionospheric imaging product over the South American region with a high spatial-temporal resolution to enable precise characterization of localized ionospheric variations and plasma gradients therein.
In response to the aforementioned challenges, we here introduce a new TEC-based ionospheric data assimilation system for 3-D regional ionospheric imaging over the South American sector (TIDAS-SA) (45°S-15°N, 35°-85°W, and 100-800 km).TIDAS-SA is developed utilizing a hybrid Ensemble-Variational algorithm and is driven by comprehensive observational data sets, including vast line-of-sight GNSS TEC observations from ∼300 ground-based receivers, radio occultation measurements from the Constellation Observing System for Meteorology Ionosphere and Climate-2 (COSMIC-2), and altimeter TEC data from the JASON-3 satellite.The regional electron density distribution is reconstructed with a spatial-temporal resolution of 1° (latitude) × 1° (longitude) × 20 km (altitude) × 5 min.The accuracy of the data assimilation results are validated against independent ionosonde and in situ measurements, and we present a case study using the TIDAS-SA to analyze a strong geomagnetic storm event on 03-04 November 2021.This high-fidelity regional data assimilation system can serve as a potent tool for reconstructing dynamic low-latitude and equatorial ionospheric structures in the 3-D domain for both the scientific research and space weather application.

Data Set Used for Assimilation
Ground-based TEC data is routinely generated at the Haystack Observatory of the Massachusetts Institute of Technology utilizing over 6,000 worldwide GNSS receivers, and the TEC data is made accessible to the community through the Madrigal data system (Rideout & Coster, 2006;Vierinen et al., 2016).In this data assimilation study for regional ionosphere imaging, our primary emphasis lies in the utilization of the massive line-of-sight (slant) TEC obtained from a network of ∼300 GNSS receivers situated across the South American region.The differential code biases (DCBs) are pre-calculated by the Madrigal system using a combination of least squares and minimum scalloping methods as described in Rideout and Coster (2006).TEC observations below an elevation of 25° were excluded from the analysis to reduce the impact of multi-path effects.Figure 1a shows the 2-D distribution of the GNSS receivers, and Figure 1b displays the spatial distribution of the slant TEC data across the 3-D domain.In this representation, corresponding TEC values are color-coded to provide visual information.
The COSMIC-2 constellation, launched in June 2019, consists of six satellites positioned in evenly spaced circular orbits at an altitude of 550 km with a low-inclination angle of 24° (Schreiner et al., 2020).The primary payload onboard each satellite is a Tri-GNSS radio-occultation system (TGRS) instrument, which is responsible for measuring various atmospheric-ionospheric parameters, such as atmospheric bending, refractivity in the troposphere and stratosphere, as well as ionospheric TEC, electron density, and scintillation (Weiss et al., 2022).In particular, the ionospheric radio occultation products are currently yielding ∼4,000 daily electron density profiles with high vertical resolution of a few kilometers.This extensive sampling primarily covers the equatorial and low-latitude regions between ±40° latitude, which are widely utilized by research and operational centers for space weather analysis and specification (e.g., Lin et al., 2020;J.-Y. Liu et al., 2022;Pedatella & Anderson, 2022).Figure 1c displays a typical 2-D projection of radio occultation tangent point over the South American sector, and Figure 1d shows the corresponding electron density profiles in the 3-D domain along the trajectory of the tangent point.
In this study, the non-negative electron density profiles above 100 km are used for data assimilation to mitigate errors stemming from the assumption of spherical symmetry in Abel inversion (Lee et al., 2012).
The Jason-3 is an ocean altimetry satellite that flies at a nearly circular orbit at an altitude of ∼1,336 km with an inclination of 66°.The range measurements from space-borne dual-frequency altimeters onboard the Jason-3 satellite, operating at Ku band (13.75 GHz) and C band (5.3 GHz), can be used to derive nadir vertical TEC data above the ocean surface along the satellite track (Brunini et al., 2005).In this study, to mitigate the observational noise originating from the altimeter, the Jason-3 vertical TEC is initially smoothed using a 30-s moving window before being assimilated (Imel, 1994).Figures 1e and 1f show an example of Jason-3 vertical TEC above the ocean in 2-D and 3-D view.The systematic biases, such as those between GNSS and Jason-3, are estimated as a daily constant value with respect to the NeQuick reference model during the inversion procedures of the data assimilation.

Data Set Used for Validation
The TIDAS-SA data assimilation results are validated against independent ionospheric measurements from four ionosonde stations in South America: Jicamarca (12°S, 76.8°W), Sao Luis (2.6°S, 44.2°W), Fortaleza (3.9°S, 38.4°W), and Cachoeira Paulista (22.7°S, 45.0°W).Figure 1a shows the locations of these ionosondes.Furthermore, the data assimilation results are also validated using pre-excluded TEC observations as well as using in situ Ne measurements given by the Ion Velocity Meter instruments onboard the Ionospheric Connection Explorer (ICON) satellite (Heelis et al., 2017).The ICON satellite flew at an altitude range of 580-610 km with an inclination angle of 27° for middle and low-latitude ionospheric and thermospheric study (Immel et al., 2018), though the mission did not provide data from November 2022 due to technical issues.

TIDAS Data Assimilation Methodology
The TIDAS is a new TEC-based ionospheric data assimilation model for reconstructing 3-D regional ionospheric electron density distribution, which assimilates the above-mentioned ground-based and space-borne TEC/Ne data into the background NeQuick model utilizing a hybrid Ensemble-Variational method (Aa, Zhang, Erickson, et al., 2023;Aa et al., 2022).TIDAS was initially developed for the continental US region (TIDAS-US) to specify the midlatitude electron density gradients therein such as the storm-enhanced density plume (Aa et al., 2022).Subsequently, TIDAS has been updated to cover the European longitude sector (TIDAS-EU) (Aa, Zhang, Wang, et al., 2023), enabling 3-D ionospheric imaging in that region as well.In this study, the TIDAS-SA data assimilation system has been further developed for the South American sector to specify the low-latitude and equatorial ionospheric dynamics.
The data assimilation technique used by TIDAS is an Ensemble-Variational method, which consists of an ensemble-based background error covariance estimation algorithm and a three-dimensional variational (3DVAR) approach.At each time step, TIDAS first computes a non-static location-dependent background error covariance using sample statistics from the ensemble of background NeQuick model outputs Here, x b represents the state variable of the background model (i.e., electron density), and N ensem refers to the ensemble numbers.The ensemble of the background model is typically created by introducing random perturbations to the main inputs/drivers through following a Gaussian-like distribution.Regarding the NeQuick model, the Ne/TEC outputs at a specific time/location primarily depend on a key proxy representing solar activity, which can be given by the 10.7 cm solar radio flux (F10.7) or monthly mean sunspot number (Nava et al., 2008).
To obtain a more realistic ensemble statistics, the input F10.7 can be flexibly defined using a variable denoted as Az, which represents the effective local ionization level and is calculated through minimizing the root mean square error (RMSE) between the modeled and observed TEC (e.g., Aa et al., 2018;Brunini et al., 2011;Nava et al., 2011).The computed Az value at each grid point is then used as the center values for Gaussian distributions with a standard deviation of 15% to create ensemble members.Consequently, the background error covariance matrix, denoted as P b , can be formulated in terms of the ensemble approach as follows (Evensen, 1994): where   are the average values of the ensemble of background model outputs.
The TIDAS system assimilates the aforementioned observation data in the measurement update step using the 3DVAR approach.3DVAR conceptualizes data assimilation as a statistical estimation problem, aiming to minimize a cost function that measures the discrepancy between the modeled state variable and observational data (Barker et al., 2004).The equations for the maximum likelihood estimation of the state variable and error covariance are shown as below: where x b and x a are the background and reanalyzed state variable (i.e., electron density), respectively.y is the observation data (i.e., TEC or Ne).H serves as the observation operator, connecting the state variable to the observation vector.P b and R are the background and observation error covariance matrices, respectively.P a is the reanalyzed background error covariance matrix.Considering that NeQuick is an empirical model without forecasting ability, we currently employ a straightforward linear ratio combination,     + (1 − β)   +1  , to do the time transition for the t + 1 step.β is a flexible ratio index and is set to be 0.2 in this study.In the future, we will test the effect of using a first-order Gauss-Markov Kalman filter to do time update, aiming to improve the relaxation of x a and P a into the next time step.Additionally, we use the covariance inflation method as mentioned in Anderson and Anderson (1999) with the inflation factor being 1.05.TIDAS output is the reanalyzed regional electron density distribution with a spatial-temporal resolution of 1° (latitude) × 1° (longitude) × 20 km (altitude) × 5 min.For more details about the aforementioned Ensemble-Variational method and TIDAS products, readers may refer to Aa et al. (2022).

Results and Validation
To showcase and evaluate the performance of the TIDAS-SA system during a space weather event, an experiment of data assimilation is conducted for a severe geomagnetic storm that occurred on 03-04 November 2021.Figures 2a-2e illustrate the temporal variations of the solar wind speed and dynamic pressure, the interplanetary magnetic field (IMF) By and Bz components, the interplanetary electric field (IEF) Ey component, the Kp and F10.7 indices, and the longitudinally symmetric (SYM-H) index during 03-05 November 2021.The geomagnetic storm was caused by several coronal mass ejections (CMEs) occurring on 01-02 November, primarily resulting from a full-halo CME associated with an M1-class solar flare eruption at 03:01 UT on 02 November.The interplanetary shock wave reached Earth's magnetosphere and triggered a storm sudden commencement at ∼19:42 UT on 03 November, with the solar wind speed suddenly increasing from 500 to 700 km/s.The IMF Bz exhibited a southward impulse during 20-22 UT on 03 November that reached −15 nT, following by an ∼8 hr fluctuation between short periods of northward and southward.After that, Bz remained southward for a long period of time yet with small intermittent fluctuations during 05-13 UT, with a minimum value of −18.7 nT at 07:20 UT on 04 November.Solar activity was at a low level in these days with the F10.7 indices being 89-92 solar flux unit (sfu, 1 sfu = 10 −22 W/m 2 /Hz).The Kp index reached 7 and 8-during 06-09 UT and 09-12 UT on 04 November, respectively.The SYM-H index exhibited two major negative peaks, which are −111 nT at 08:25 UT and −117 nT at 13:00 UT on 04 November, respectively.Several previous studies have reported that this geomagnetic storm triggered notable low-latitude ionospheric disturbances, especially over the South American sector (Rukundo, 2023;K. Wu et al., 2023;Zhai et al., 2022).This provides a good opportunity to assess our newly developed TIDAS-SA regional data assimilation system and conduct an in-depth analysis of the storm-induced ionospheric perturbations.
Figures 3a-3c display an example of TIDAS-SA data assimilation result, showcasing the 3-D ionospheric imaging over the South American sector at 16:10 UT on 03 November 2021, which is a quiet-time snapshot before the geomagnetic storm.Specifically, Figure 3a displays the reanalyzed electron density distribution at an altitude of 300 km.The double-crest structures of EIA can be clearly seen in the reconstructed results at this altitude, with the plasma densities at the crests ranging between 1.2 and 1.7 × 10 12 /m 3 .Figure 3b illustrates the shaded contour of the distribution of F2-layer peak height (hmF2) and peak density (NmF2), which demonstrates the characteristics of the typical equatorial fountain effect with ridge-like high hmF2 in the geomagnetic equatorial region and large NmF2 values in the crests region.Moreover, Figure 3c shows the TEC distribution in a global view, with the EIA crests intensity being about 35-45 TEC unit.To demonstrate the difference of TIDAS results with respect to the NeQuick model, Figures 3d-3f show the corresponding percentage differences between data assimilation results and the NeQuick model.It is evident that TIDAS results exhibit more dynamic regional fluctuations with considerable improvement compared to NeQuick results, which are 10%-25% higher at the EIA crests region and are 10%-25% lower at the trough and poleward side of EIA.These initial results demonstrate that TIDAS data assimilation system can effectively reconstruct the 3-D ionospheric morphology of EIA-related structures with both large-scale features and meso-scale details in the equatorial and low-latitude ionosphere over the South American region.
To better investigate the storm-time ionospheric disturbances, Figure 4 shows the TIDAS data assimilation results at the same UT interval as that of Figure 3 but on the storm day of 04 November 2021.Through a comparison of Figures 3a-3c and 4a-4c, along with examining the percentage differences between TIDAS results and NeQuick climatology (Figures 4d-4f), it can be seen that the storm-time low-latitude ionosphere was characterized by a strong positive storm phase (enhanced electron densities).The magnitude of electron density around the EIA crests on the storm day is about 30%-50% larger than that of the quiet day.The storm-time hmF2 in the vicinity of equatorial region is 40-60 km higher than that of the quiet-time counterpart.The magnitude of storm-time TEC enhancements is about 40%-60% in the EIA crests region and 20%-30% in the equatorial trough region.This positive ionospheric storm was also reported by Zhai et al. (2022) using 2-D ground-based GNSS TEC and 1-D in situ measurements, which are consistent with our 3-D ionospheric imaging results.
To illustrate the 3-D ionospheric morphology more comprehensively, Figure 5 presents the reanalyzed regional Ne maps at various altitudes between 200 and 600 km at four UTs during 12:00-16:30 UT on 04 November 2021, covering the late main and early recovery phase of the storm.Likewise, Figure 6 depicts the corresponding altitude-latitude slices of the regional Ne at different longitudes.These images clearly demonstrate that the TIDAS data assimilation results provide a well-defined representation of the 3-D ionospheric dynamic structures, such as the development and evolution of EIA morphology.The TIDAS results reveal that the intensity of EIA crests were gradually amplified during the selected time period, which exhibited a double-peak structure generally in the F2 region and lower topside ionosphere and merged into a single-peak structure as altitude increases in the upper topside ionosphere.These data assimilation results offer crucial altitude information across the bottomside and topside ionosphere over the low-latitude and equatorial region for analyzing ionospheric space weather events.These large scale 3-D variations were not previously reported from a single-instrument observation.
To further leverage the results of data assimilation for analyzing the storm-time low-latitude and equatorial ionospheric disturbances, Figures 7a-7f show reanalyzed regional maps of differential NmF2 and differential hmF2 values at four UTs on 04 November 2021, respectively.These differential values are calculated by subtracting 10.1029/2023SW003792 9 of 17 the reference values (using averaged TIDAS results from two geomagnetically quiet days before the storm) from the values during the storm.At 12:00 UT, the storm-time NmF2 and hmF2 showed a 30%-50% increase and a 10-20 km rise in altitude within the ±15° geomagnetic latitudes (Figures 7a and 7e).This indicates a positive ionospheric storm phase occurring in the equatorial and low-latitude ionosphere over the South American sector.Subsequently, at 13:30 UT and the following UTs, after the Sym-H index dropped to a minimum value of −117 nT, the NmF2 and hmF2 values in the equatorial and low-latitude regions further increased by 60%-100% and 20-60 km, respectively.This strong positive ionospheric storm phase with noticeable enhancement in NmF2 and elevation in hmF2 was observed following the southward excursion of IMF Bz during 10-13 UT on 04 November 2021.These results suggest that an enhanced eastward electric field component and upward E × B drifts, resulting from the penetration electric field that led to the ionosphere being lifted to a higher altitude with a lower recombination   rate, could be one of key drivers causing this positive ionospheric storm.The data assimilation results align well with observations made by Zhai et al. (2022), who used the ionosonde and ICON drift measurements to prove the aforementioned electrodynamic effect.Moreover, Zhai et al. (2022) reported a ∼50% enhancement in O/N 2 in the equatorial and low-latitude regions of South America, as observed by the Global-scale Observations of the Limb and Disk (GOLD) satellite.It is known that the storm-time altered global circulation pattern tends to reduce the neutral density ratio O/N 2 at mid-to-high latitudes as nitrogen-rich air ascends through constant pressure surfaces, while the O/N 2 ratio normally increases at equatorial and low-latitudes due to the downwelling of atomic oxygen equatorward of the composition disturbances zone and the transport of composition disturbances from high latitudes toward the lower latitudes by the equatorward winds (Prölss, 1980(Prölss, , 2008)).Such a thermospheric composition variation also contributed to the observed positive ionospheric storm over the South American sector.
We next validate the TIDAS data assimilation results using independent observations from four ionosondes at Jicamarca (12°S, 76.8°W), Sao Luis (2.6°S, 44.2°W), Fortaleza (3.9°S, 38.4°W), and Cachoeira Paulista (22.7°S, 45.0°W).The locations of these ionosondes are showed in Figure 1a. Figure 8 displays the electron density profiles obtained from these ionosonde measurements, background NeQuick model, and TIDAS data assimilation results.The results reveal that the NeQuick model can merely capture a general diurnal variation pattern of the ionosphere (Figure 8b), as NeQuick does not include storm effects.As can be seen, there are large deviations between the NeQuick profiles and the ionosonde observations (Figure 8a).On the contrary, the TIDAS data assimilation results (Figure 8c) demonstrate a substantial improvement that exhibits significantly better agreement with ionosonde measurements, which effectively reproduced the fine structures and dynamic ionospheric disturbances over the South American region during the storm.For example, the TIDAS results effectively captured a feature of the enhanced postsunset rise of the equatorial F-layer at the Jicarmaca station around 22-24 UT on November 03.This phenomenon was likely caused by a combination of the storm-induced prompt penetration electric field and the pre-reversal enhancement.Moreover, the TIDAS results represent a notable positive ionospheric storm phase for those stations during 12-18 UT on November 04, with F2-region Ne values being 20%-50% higher compared to the same UTs on the previous day.These data assimilation results of the positive ionospheric storm phase are generally consistent with both ionosonde measurements.However, it is worth noting that these automatic ionosonde data contain sporadic data gaps and outliers, which may introduce potentially large uncertainties.Additionally, the topside ionosonde profiles were not realistic observations but were derived assuming an alpha-Chapman function of plasma distribution (Reinisch & Huang, 2001).These factors could partially account for certain discrepancies observed between the ionosonde profiles and the data assimilation results.
To quantitatively evaluate the systematic improvement with TIDAS data assimilation, Figures 9a and 9b display a comparison of histogram statistics for the differential NmF2 between those four ionosonde measurements and NeQuick values as well as TIDAS data assimilation results during 03-04 November 2021.As depicted, the differential NmF2 between ionosonde and NeQuick values exhibits a more dispersed distribution with a relatively large standard deviation value (3.72 × 10 11 /m 3 ).In contrast, the differential NmF2 between ionosonde measurements and TIDAS data assimilation results shows a noticeable improvement with a narrower distribution and a smaller standard deviation (2.2 × 10 11 /m 3 ).To further assess the performance of TIDAS data assimilation, we here randomly selected approximately 10% of the TEC observations as a control group.These observations were not used for data assimilation but were reserved for validation purposes.Figures 9c and 9d show a comparison of histogram statistics for the differential TEC values between Madrigal GNSS observations and those retrieved from the NeQuick model and TIDAS data assimilation results.While the NeQuick modeled values show a more dispersed distribution with a larger standard deviation value of 6.31 TECU, the TIDAS data assimilation results exhibit a significant systematic improvement, displaying a nearly unbiased and much narrower distribution with a significantly smaller standard deviation value of 0.91 TECU.These results serve as the compelling evidence that demonstrates the effectiveness of TIDAS data assimilation.
To assess the performance of TIDAS data assimilation in the topside ionosphere, Figure 10 shows regional Ne maps reconstructed by TIDAS at an altitude of 600 km, overlapping with the ICON satellite path at six different UT intervals ranging from 12:20 UT to 20:55 UT on 04 November 2021.The lower subpanels depict the corresponding longitudinal Ne profiles, with black lines representing ICON in situ measurements (black), red lines representing the TIDAS data assimilation results, and blue lines for NeQuick values.The NeQuick climatology values showed significant discrepancies compared to the storm-time observations, sometimes reaching as large as 50%-80% as illustrated in Figures 10b and 10c.In contrast, the TIDAS-reconstructed Ne agrees quite well with the ICON in situ profiles, effectively capturing the equatorial and low-latitude ionospheric variations over the South American sector.Although Figures 10b and 10f show that there are few instances where TIDAS and ICON Ne profiles can sometimes exhibit moderate deviations of 20%-30%, the trends in their longitudinal variations remain quite consistent with each other.This demonstrates the accuracy of TIDAS data assimilation in specifying the topside ionosphere.

Conclusions
In this study, we have developed a new TEC-based ionospheric data assimilation system for the 3-D ionospheric imaging in the equatorial and low-latitude regions over the South American sector (TIDAS-SA).The TIDAS-SA data assimilation system employs a hybrid Ensemble-Variational approach and utilizes a wide range of observational data sources, including dense ground-based GNSS line-of-sight TEC data, COSMIC-2 radio occultation measurements, and JASON-3 altimeter TEC data.This amalgamation of data sources enables TIDAS to reconstruct the electron density distribution in a 3-D domain over South America, with a spatial-temporal resolution of 1° × 1° in latitude and longitude, 20 km in altitude, and 5 min in universal time.The performance and reliability of the data assimilation results are assessed based on a case study for a strong geomagnetic storm event on 03-04 November 2021.In particular, for validation, we compared TIDAS-SA results with independent ionosonde data, pre-excluded TEC observations, and in situ measurements from the ICON satellite.The results indicate that the TIDAS-SA data assimilation system can effectively represent the storm-time ionospheric dynamics and accurately reproduce the positive ionospheric storm phase over the South American region in the 3-D domain.This capability makes TIDAS-SA a valuable tool for providing detailed, altitude-resolved information that can contribute to the advancement of our current understanding of storm-time ionospheric response and multi-scale structures in the equatorial and low-latitude ionosphere.Furthermore, it is worth noting that the storm-time electron density variation in the upper ionosphere and the plasmasphere could be as significant as that in the lower region.In the future, we aim to further raise the upper altitude boundary of the data assimilation system by incorporting more data sets from the upper ionosphere and/or plasmasphere, such as the DMSP in situ measurements and topside TEC data from low-Earth orbiting satellites.

Figure 1 .
Figure 1.The data sets distribution for the case study on 04 November 2021 that are used for TIDAS data assimilation: (a) Distribution of ground-based GNSS receivers (red dots), overlapping with four ionosondes (black stars).(b) 15-min coverage of slant TEC paths of ground-based GNSS receivers.(c and d) 1-hr coverage of COSMIC-2 radio occultation tangent point 2-D traces and corresponding 3-D electron density profiles.(e and f) JASON vertical TEC over the ocean in 2-D and 3-D format.The TEC/Ne values are color-coded.

Figure 3 .
Figure 3. 3-D ionospheric imaging over the South American region at 16:10 UT on 03 November 2021 that provided by the TIDAS data assimilation system: (a) electron density distribution at 300 km; (b) distribution of ionospheric F2-layer peak height (hmF2) and peak density (NmF2); (c) reanalyzed regional TEC.The terminator (red line) and specific geomagnetic latitude lines are marked.(d-f) Are the same as (a-c), but for the percentage differences between TIDAS data assimilation results and NeQuick values.

Figure 4 .
Figure 4.The same as Figure 3, but for the geomagnetic storm day on 04 November 2021.

Figure 6 .
Figure 6.(a-d) The same as Figure 5, but for latitude/altitude Ne slices at different longitudes.

Figure 9 .
Figure 9. (a and b) Comparison of histogram statistics for the F2-layer peak density (NmF2) between ionosonde measurements and those retrieved from the NeQuick model and TIDAS data assimilation results during 03-04 November 2021.(c and d) Comparison of histogram statistics for the differential TEC between Madrigal data and those obtained from the NeQuick model and TIDAS data assimilation results.

Figure 10 .
Figure10.(a-f) TIDAS-reconstructed regional Ne maps at an altitude of 600 km with overlapping ICON path at six UT intervals on 04 November 2021.The bottom subpanels show the corresponding longitudinal Ne profiles given by ICON in situ measurements (black), TIDAS data assimilation results (red), and NeQuick values (blue).