1 Introduction

Ionospheric models are essential for correcting pseudo range errors in single-frequency global navigation satellite systems (GNSS) applications. Among these, the vertical total electron content (VTEC) stands out as an important ionospheric parameter for space weather investigations and real-time, high-precision positioning, such as precise point positioning real-time kinematic (PPP-RTK) services (Klobuchar 1987; Hirokawa and Fernández-Hernández 2020; Li et al. 2020). There are several analytical centers providing routinely updated VTEC maps, notably the global ionospheric map (GIM), based on data from global GNSS ground stations (Hernández-Pajares et al. 2009). However, the uneven distribution of ground stations, particularly sparse over oceans and deserts, results in degraded model accuracy in these regions. Besides the ground-based observations, ionospheric parameters can also be retrieved from spaceborne measurements, such as intersatellite links. GNSS/low Earth orbit (LEO) radio occultation (RO) is a well-established technique providing ionospheric soundings with low cost, global coverage and high precision. While RO offers vertical profiles of electron density, satellite altimetry (SA) observes marine areas, furnishing VTEC measurements along the nadir track via dual-frequency signals. The integration of multi-source data through data assimilation or combination methods provides a compelling opportunity to enhance operational ionospheric models (Alizadeh et al. 2011; Chen et al. 2017). Nevertheless, these data are obtained through diverse techniques and processing methods, resulting in discrepancies in resolution, coverage, accuracy and time latency among direct ionospheric products. Understanding the accuracy and bias inherent in different observation techniques is crucial for determining the weights in data combinations. Similarly, constructing an error covariance matrix in data assimilation also requires reliable accuracy information to appropriately balance the contributions from background models and realistic measurements (Bust et al. 2004; Aa and Zhang 2022).

In earlier literatures, observations from SA and RO have often been utilized as independent validation data to assess global ionospheric TEC maps and empirical models, with less emphasis on their inherent differences (Brunini et al. 2005; Cherniak and Zakharenkova 2019; Li et al. 2019; Wielgosz et al. 2021). Some researches addressed the systematic TEC discrepancies among GNSS, spaceborne and other space-geodetic techniques: Li et al. (2019) analyzed the bias and scaling factors between International GNSS Service (IGS) GIM and spaceborne TEC, noting variations with season, local time and location; Alizadeh et al. (2011) developed GIM from GNSS, satellite altimetry and radio occultation data, adopting empirical weighting schemes and a priori variances for various VTEC observations without detailed discussion on technique differences; Dettmering et al. (2011b) applied variance component estimation method to account for accuracy differences among terrestrial and satellite-based GNSS, DORIS, altimetry and VLBI, focusing on a specific region around the Hawaiian Islands during a 2-week interval in 2008 and Chen et al. (2017) integrated ground- and space-based data similarly and estimated the instrumental bias and plasmaspheric component of different ionospheric data as 2-h or daily constant parameters in May 2013.

The systematic differences among TEC datasets are mainly caused by modeling errors, unknown hardware offsets and variations in observation geometries. For GIMs, absolute VTEC may be affected by mapping function errors and estimation error of differential code bias (DCB). RO observations employ dual-frequency combinations of excess phase to obtain relative TEC observations, with electron density retrieved via Abel inversion. While the integral VTEC is free of DCB estimation error, it suffers from retrieval errors due to the spherical symmetric assumption. On the other hand, the dual-frequency altimeter onboard the SA platform directly measures the ionosphere in the nadir direction, allowing VTEC extraction without mapping function application. However, systematic bias from consecutive missions and different data versions should be handled with cares when using SA TEC observations as references. Additionally, the vertical coverage of these datasets introduces inherent bias among different TEC results. Ground-based GNSS VTEC measures the total ionospheric contribution from ground stations to GNSS satellite height, while RO- and SA-derived TECs cover only the vertical range below LEO orbit altitude. The contribution of the plasmasphere is non-negligible under certain circumstances, such as during nighttime in low solar activity (LSA) years (Jin et al. 2021). It is a compromise to directly compare and assess the accuracy of observations with such large vertical gaps.

Therefore, comprehensive research on the differences and validation of TEC observations is still needed on a global scale and over a longer duration, while also accounting for the influence of vertical range differences. This study aims to address these shortcomings and appropriately fill the vertical data gaps for the first time. The latest processed ionospheric data, JASON-1 ‘E’ (J1E), are regarded as the most reliable reference level among altimeter satellites, with a discrepancy of just 0.1 TECU compared to DORIS observations (Azpilicueta and Nava 2021). When conducting comparisons, we mapped the results of all the considered satellites to the J1E TEC reference frame. To mitigate the influence of orbit differences, we extrapolated the RO VTEC to the same altitude as Jason observations using an exponential profiler. Additionally, the vertical difference between RO and GIM is compensated by adding the plasmaspheric electron content above the LEO satellites. This approach enables the evaluation of TEC from different observing geometries under the same conditions and is considered to provide systematic bias-free results.

The main objectives of this research can be summarized as follows:

  1. (a)

    Investigating the intermission bias of altimetry TEC observations, including the Jason and Sentinel series, and determining the reference standard and accuracy level for global TEC comparison (Sect. 3);

  2. (b)

    Comparing the TEC observations from satellite altimetry and Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) radio occultation with the same vertical coverage under different solar activity conditions in oceanic regions (Sect. 4);

  3. (c)

    Assessing the GIM VTEC in various latitudinal bands and ocean/land locations based on local time, seasons and solar activity levels, while considering compensated COSMIC observations that account for the plasmaspheric contribution (Sect. 5);

  4. (d)

    Analyzing specific ionospheric characteristics revealed by different observation techniques and addressing the advantages and disadvantages of each method (Sect. 6).

The assessment of TEC measurements in this study may provide insights for specifying weights and error variances in data combination and data assimilation processes.

2 Data sources and methods

The data considered in this study comprise VTEC observations from Jason-1/2/3 and Sentinel-3 satellites, COSMIC-retrieved TEC and ground-based GIM. Figure 1 provides an overview of the data coverage and maximum observing altitudes of these TEC datasets. The data continuity of GNSS ground stations is the most consistent, while Jason and COSMIC data have been available only since 2006. The satellite altitudes vary across missions, with COSMIC-1 orbiting at approximately 800 km and COSMIC-2 at 500 km after constellation deployment. The Sentinel-3A, available since 2016, orbits at the similar altitude of COSMIC-1, while the Jason series remains at approximately 1330 km altitude. To encompass the solar cycle revolution and periods of overlap among different techniques, we selected the years 2008 and 2014 to represent low and high solar activity conditions. The Sentinel series of satellites provide a vital contribution to Earth monitoring these years. To ensure a sufficient volume of co-located observations with RO, we chose the year 2017 for comparisons among COSMIC, Jason and Sentinel satellites. Methods for leveling the vertical coverage of different TEC datasets to the same altitude are introduced in detail below.

Fig. 1
figure 1

The satellite altitude and temporal coverage of COSMIC, Jason, Sentinel series and GNSS observations over recent decades

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2.1 GIM VTEC

GIM provides global vertical TEC from the ground to GNSS satellites and finds application in various fields such as real-time ionospheric error mitigation, space weather and climate monitoring. It is also regarded as a validation reference for other data types or empirical models (Hernández-Pajares et al. 2009). GIMs have been systematically produced and provided by the international GNSS service ionosphere working group (IIWG) since June 1, 1988. Different ionospheric-associated analysis centers (IAACs) develop their own GIM products using various methodologies and standards. The final IGS product is a weighted combination of individual GIMs provided by these IAACs, with specific spatial and temporal resolutions (typically \(2.5^\circ lat \times 5.0^\circ lon\), 15 min to 2 h). The assessment of the accuracy and consistency of different techniques, estimations and GIM products has been crucial in recent years, considering various solar conditions, geographical locations, interpolation methods and mapping functions (Hernández-Pajares et al. 2017; Roma-Dollase et al. 2018; Li et al. 2019; Wielgosz et al. 2021). In this study, we utilize the IGS GIM with a 2-h temporal resolution. Figure 2 illustrates the IGS ground stations used to construct the ionospheric maps and the distribution of GIM VTEC. The stations are relatively denser in the Northern Hemisphere and on land in Europe and America, while sparser over oceans and in polar regions. Consequently, the accuracy of GIM in the ocean-dominated Southern Hemisphere is anticipated to degrade to some extent.

Fig. 2
figure 2

The distributions of ground IGS stations (gray triangles) and the GIM VTEC. The selected time is UT 0:00 on DOY 137 of 2014

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2.2 COSMIC VTEC

COSMIC/FORMOSAT-3 is a US‐Taiwan joint radio occultation mission consisting of six satellites. Launched in April 2006, COSMIC has provided numerous neutral atmospheric and ionospheric sounding data, making a great contribution to operational numerical weather prediction and ionospheric research (Anthes et al. 2008). The spaceborne RO receiver receives dual-frequency signals, enabling the calculating of relative TEC along the signal trajectory from the LEO receiver to the GNSS transmitter by combining phase measurements at two frequencies of each system (\(L_{1}\) and \(L_{2}\)):

$${\text{TEC}} = \frac{1}{40.3}\frac{{f_{1}^{2} f_{2}^{2} }}{{f_{1}^{2} - f_{2}^{2} }}\left( {L_{1} - L_{2} } \right)$$
(1)

where \(f_{i}\) represents the signal frequency; and \(L_{i}\) is the phase measurement at each frequency. To obtain calibrated TEC, the contribution of electron above the LEO orbit height should be excluded. This calibrated TEC represents the integral of electron density along the line of sight. Usually, the Abel transformation is applied to retrieve electron density at each tangent point height from the TEC observations under assumption of ionospheric spherical symmetry. The COSMIC Data Analysis and Archive Center (CDAAC) is responsible for data processing of COSMIC and several other occultation missions. A follow-on satellite mission, COSMIC-2 (FORMOSAT-7), was successfully launched on June 25, 2019 (Schreiner et al. 2020). Pedatella et al. (2021) processed and validated COSMIC-2 absolute TEC observations by comparing them with collocated Swarm-B TECs, concluding that TEC accuracy was better than 3.0 TECU. Satellite data and products of various levels are provided in an open-access environment hosted by CDAAC. In this study, we focus on VTEC, which is obtained by the integral of the vertical electron density profile (EDP) along the vertical path. However, EDP suffers from the retrieval errors due to the ionospheric spherical symmetry assumption in the Abel inversion (Yue et al. 2010). Thus, instead of directly using the level 2 products from CDAAC, we collected COSMIC level 1b observations and performed an IRI-aided (IRI for International Reference Ionosphere) Abel inversion to estimate more precise EPDs. Under high solar activity (HSA) conditions, the new Abel inversion demonstrates a significant improvement of more than 1 TECU over the classic retrieval approach (Wu et al. 2019). The main processing procedures are summarized as follows:

  1. (1)

    Step 1, Classic Abel inversion: The COSMIC RO excess phase observations (labeled as ‘ionPhs’ file in level1b) are processed and retrieved by standard Abel inversion to obtain electron density at each tangent point;

  2. (2)

    Step 2, Parameter modeling: Three F2-layer parameters (the critical frequency (foF2), the peak density height (hmF2) and the scale height (Hsc)), and two topside parameters (the TEC above the satellites and the topside electron density), are extracted from the EDPs and modeled by spherical harmonics expansion and empirical orthogonal functions;

  3. (3)

    Step 3, IRI improvement: The modeled foF2 and hmF2 models are integrated into IRI as new choices for the F2 peak parameters; the scale height and adaptive topside parameters are incorporated into the IRI topside function; subsequently, an enhanced IRI model, constrained by external data from RO, is constructed (Wu et al. 2018);

  4. (4)

    Step 4, Aided Abel inversion: The enhanced IRI model serves as a background field, providing additional horizontal gradient information. The classic Abel inversion is improved by adopting a spherical symmetric TEC constraint (Guo et al. 2015; Wu et al. 2019);

  5. (5)

    Step 5, Iteration: All steps can be run iteratively to gradually reduce ionospheric retrieval errors.

Since the vertical range associated with the TEC obtained from ground-based GNSS receiver, COSMIC RO and satellite altimetry varies, direct comparison of TEC from these three sources is not meaningful. To compensate for the contribution of the topside ionosphere and plasmasphere above RO satellites, precise orbit determination (POD) observations of COSMIC (labeled as ‘podTec’ in CDAAC) are utilized to fill the TEC gap above the RO satellites up to the GNSS satellites. The distribution of RO and POD observations and their corresponding TEC are shown in Fig. 3. RO measurements exhibit good global coverage over both land and oceans. Panel (b) illustrates the spatial characteristics of plasmaspheric TEC at midnight, with their contribution potentially exceeding 10 TECU at mid- and low latitudes. It should be noted that the RO TEC is assumed to be located at the position (longitude and latitude) of peak electron density, while POD yield TEC is observed at the position of LEO satellite. To connect the two TECs, POD STEC with elevation angle greater than 50° is converted to VTEC using the F&K mapping function (Foelsche and Kirchengast 2002), and a global gridded model is constructed based on latitude, local time, month and year in step 2.

$${\text{VTEC}}_{{{\text{POD}}}} = \frac{{1 + R_{{{\text{shell}}}} /R_{{{\text{orbit}}}} }}{{\sqrt {\left( {R_{{{\text{shell}}}} /R_{{{\text{orbit}}}} } \right)^{2} - {\text{sin}}^{2} \left( z \right)} + {\text{cos}}\left( z \right)}} \times {\text{STEC}}_{{{\text{POD}}}}$$
(2)

where \(R_{shell}\) is the radius of the effective height, applying 2100 km here (Zhong et al. 2016); \(R_{orbit}\) is the radius of LEO satellite and \(z\) is the zenith angle of the line-of-sight ray. When comparing RO to ground-based GIM VTEC, the actual COSMIC VTEC comprises the following two components:

$${\text{VTEC}}_{{{\text{RO}}}} = {\text{TEC}}_{0} + {\text{TEC}}_{1} = \mathop \int \limits_{0}^{{h_{{{\text{RO}}}} }} Ne\left( h \right)dh + {\text{VTEC}}_{{{\text{POD}}}}^{\prime }$$
(3)

in which \(TEC_{0}\) represents the integral TEC of the RO electron density profile (\(Ne\left( h \right)\)), and \(TEC_{1}\) is the specific \(VTEC_{POD}\) matched to the position of \(TEC_{0}\) by interpolation of POD VTEC model, denoted as \({\text{VTEC}}_{{{\text{POD}}}}{\prime}\).

Fig. 3
figure 3

The distribution of a COSMIC RO and b POD VTEC in January 2014, LT 0:00 ~ 2:00

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2.3 Satellite altimetry VTEC

Jason is a collaborative oceanography serial mission of the Centre National d’Etudes Spatiales (CNES) and the National Aeronautics and Space Administration (NASA), with the aim of monitoring global ocean circulation, understanding the tie between oceans and the atmosphere, improving global climate prediction and investigating phenomena such as El Niño conditions and ocean eddies (Lafon and Parisot 1998). Jason-1 was successfully launched in December 2001 and provided precise measurements of sea-surface elevation until June 2013. Its follow-on missions, Jason-2 and Jason-3, were launched in June 2008 and January 2016, respectively, and have continued to operate effectively since their launches. Sentinel-3 is a dedicated satellite mission under the Copernicus program, providing high-quality ocean and atmosphere measurements such as sea-surface topography, sea-surface temperature and ocean surface color. Sentinel-3A was launched on February 16, 2016, equipped with an altimeter instrument called Synthetic Aperture Radar Altimeter (SRAL) onboard. In addition to its primary oceanography objectives, spaceborne dual-frequency altimeters aboard transmit signals vertically toward the sea surface, penetrating the ionosphere below the satellite’s orbit height. Therefore, the SA VTEC can be calculated according to the following formula:

$${\text{VTEC}} = - \frac{{dR \cdot f^{2} }}{40.3}$$
(4)

where \(dR\) represents the ionospheric range correction of the Ku or C band, and \(f\) is the band frequency. For Jason, the \(dR\) is provided in the geophysical data records and is available for registered users at the CNES website https://aviso-data-center.cnes.fr. The ionospheric correction products of Sentinel-3 in the marine areas are operationally managed by the EUMETSAT Sentinel-3 Marine Centre (https://www.eumetsat.int/eumetsat-data-centre). The original ionospheric correction may be affected by instrument noise effects; therefore, we applied a filter of 20–25 samples along the orbit track, as recommended by the product handbook and Imel (1994). The previous studies have combined satellite altimetry TEC observations with other data types to construct global or regional ionospheric models (Alizadeh et al. 2011; Dettmering et al. 2011a; Yao et al. 2018), or treated SA data as a means of accurate validation for GNSS and RO TECs, albeit with systematic bias (Li et al. 2019; Pedatella et al. 2021).

Since COSMIC and satellite altimetry measurements have different spatial and temporal distributions, the collocated comparison pairs should be matched with the following criteria: difference within \(2.5^\circ\) and a time span within 20 min. The distribution of matched footprints during an entire Jason-1 cycle (approximately 10 days) is depicted in Fig. 4. Due to differences in satellite designs, the matched points are less distributed in the equatorial area or near the poles. Sentinel-3 operates at a similar orbit altitude as COSMIC-1 satellites, allowing for direct comparison of TEC. Nevertheless, the variance in orbit height between COSMIC-1 and Jason satellites (800 km and 1300 km, respectively) introduces systematic deviations in their TECs. To mitigate the influence of orbit differences, we extrapolated the COSMIC VTEC to the same altitude as the Jason observations using an exponential profiler. The electron density above the COSMIC satellite can be represented by

$$Ne\left( h \right)^{\prime } = Ne\left( {h_{RO} } \right) \cdot {\text{exp}}\left( { - \frac{{h - h_{{{\text{RO}}}} }}{{H_{P} }}} \right)$$
(5)

where \(h_{RO}\) is the orbit altitude of the COSMIC satellite, \(Ne\left( {h_{RO} } \right)\) is the electron density at \(h_{RO}\) and \(H_{P}\) is the plasmaspheric scale height, which is already calculated in our earlier work based on COSMIC electron density profiles and POD TEC of 8 years (Wu et al. 2021). Then, the VTEC with the same vertical range of Jason observations is obtained as follows:

$${\text{VTEC}}_{{{\text{RO}}}}^{\prime } = {\text{TEC}}_{0} + {\text{TEC}}_{2} = \mathop \int \limits_{0}^{{h_{{{\text{RO}}}} }} Ne\left( h \right)dh + \mathop \int \limits_{{h_{{{\text{RO}}}} }}^{{h_{{{\text{ALT}}}} }} Ne\left( h \right)^{\prime } dh$$
(6)

in which \(h_{{{\text{ALT}}}}\) is the orbit altitude of the Jason satellite.

Fig. 4
figure 4

The collocated TEC measurements for COSMIC (black pentagram) and Jason-1 (colormap) during December 17 and 27, 2008, for an entire cycle of Jason passes

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3 Intermission bias of satellite altimetry VTEC

The systematic bias issue in altimetry TEC observations has persisted since the launch of TOPEX/Poseidon in the 1990s and continues throughout subsequent Jason missions. Differences between satellites and various versions are caused by changes in models and algorithms applied in each round of processing. To investigate the discrepancy in Jason-1, Jason-2, Jason-3 and Sentinel-3 VTEC measurements, we selected available VTEC in the same period from 2008 to 2018 (encompassing an entire solar cycle) and calculated the mean TEC for each mission (see Fig. 5). The latest and reprocessed data versions were utilized where available, denoted as ‘E’ for Jason-1, ‘D’ for Jason-2 and ‘F’ for Jason-3 (Azpilicueta and Nava 2021), and the 2019 reprocessed version for Sentinel-3. According to Fig. 5, the Jason-2 VTEC is higher than all other missions throughout the last solar cycle. During the overlap periods of Jason-1 and Jason-2 from 2008 to 2010, VTEC differences are relatively stable, ranging from 2.939 to 3.502 TECU. The differences seem less correlated with the solar activity variations, since the discrepancy from 2008 to 2013 is not enlarged even though the absolute TEC notably increases under the high solar activity conditions. From 2016 onwards, we have simultaneous measurements from Jason-2, Jason-3 and Sentinel-3. Results indicate that Jason-2 VTEC remains highest among all satellite series (Wielgosz et al. 2021). The mean VTEC of Sentinel-3 is higher than that of Jason-3 but lower than that of Jason-2. In the year 2017, the average discrepancy of Jason-2 and Jason-3 is 3.52 TECU, while decreasing to 1.67 TECU between Jason-2 and Sentinel-3.

Fig. 5
figure 5

The mean TEC of Jason-1, Jason-2 and Jason-3 and Sentinel-3. The mean F10.7 index in each year is shown by the dashed read line according to the right y-axis

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The systematic bias observed in intermission comparisons for Jason satellites is coherent with results obtained from the official validation and cross-calibration activities. According to annual reports of different Jason missions and versions, the relationships between Jason-1/2/3 are as follows: \({\text{Jason2}}_{D} \gg {\text{Jason1}}_{E} { + 3}{\text{.4 TECU}}\) and \({\text{Jason3}}_{T} \gg {\text{Jason2}}_{D} { - 2}{\text{.5 TECU}}\), where the subscript represents the data version (Roinard and Lievin 2017; Roinard and Michaud 2020). However, the TEC of the latest Jason-3 version, denoted as \({\text{Jason3}}_{F}\), shows a mean difference of about 3.98 TECU lower than \({\text{Jason2}}_{D}\). Azpilicueta and Nava (2021) concluded that \({\text{Jason1}}_{E}\) was the most accurate, with the least absolute bias of approximately 1 TECU relative to DORIS. Therefore, Jason-1 VTEC can be considered as a standard for mapping other datasets into \({\text{Jason1}}_{E}\) reference frame. In the following study, we will apply intermission correction based on the mean difference obtained from Fig. 5 to eliminate the systematic bias from the Jason and Sentinel TEC observations:

$$\begin{array}{*{20}c} {{\text{JASON}}2_{D} \approx {\text{JASON}}1_{E} + 3.4 {\text{TECU}}} \\ {{\text{JASON}}3_{F} \approx {\text{JASON}}1_{E} - 0.12 {\text{TECU}}} \\ {{\text{SENTINEL}}3 \approx {\text{JASON}}1_{E} + 1.73 {\text{TECU}}} \\ \end{array}$$
(7)

4 Comparison between satellite altimetry and RO VTEC

4.1 The daily differences between Jason and COSMIC VTEC

There is an overlap of approximately 6 months between Jason-1 and Jason-2 in 2008, as Jason-2 officially launched in July. We collected available TEC data from both Jason missions and matched them with COSMIC VTEC measurements. \({\text{VTEC}}_{{{\text{RO}}}}^{\prime }\) with topside compensation was utilized, assuming no remaining bias due to the altitude difference between the RO and SA satellites. The mean bias and standard deviation (STD) were calculated in each day based on all differences of coincident COSMIC and Jason TEC, as shown in Fig. 6. According to the mean bias represented by the green line, the VTEC values of COSMIC and Jason-1 agree well with each other in 2008, with biases of less than 1 TECU. However, later this year, when directly comparing to the original Jason-2 VTEC (represented by the brown line), the RO results demonstrate a notable underestimation, with COSMIC-Jason residuals varying around -3 TECU. It confirms that the systematic bias between Jason missions can reach several TEC units. Given the systematic bias of altimetry missions studied in Sect. 3, the correction application between Jason-1 and Jason-2 is demonstrated in panel (b), where ‘JASON2c’ is mapped to the Jason-1 reference frame by subtracting 3.4 TECU from the original Jason-2 values. Consequently, COSMIC demonstrates very good agreement with both Jason ionospheric products. The STD of the VTEC among different missions is not influenced by the systematic bias, and COSMIC differs from Jason by 1 ~ 3 TECU. Seasonal variations are not pronounced under LSA condition.

Fig. 6
figure 6

The variations in VTEC differences among COSMIC, Jason-1 and Jason-2 in 2008. Panels a and b are the daily mean bias, and ‘JASON2c’ indicates the corrected Jason-2 VTEC; panel c is the STD

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Figure 7 shows similar results but under higher solar activities in 2014 when only Jason-2 data are available. The bias of COSMIC increases to -5 TECU during the equinox seasons in comparison with the Jason-2 VTEC. However, when the Jason-2 observations are corrected by systematic bias, the underestimation of COSMIC VTEC is significantly mitigated. Given the absolute accuracy of Jason-1 TEC measurements, COSMIC RO data can be considered high-precision ionospheric measurements under different solar activity conditions. The seasonal variations in STD are more pronounced in 2014, with greater deviations and higher discrepancies in spring and autumn, during the equinox seasons.

Fig. 7
figure 7

The variations in VTEC differences among COSMIC and Jason-2 in 2014. Panels a and b are the daily mean bias, and ‘JASON2c’ indicates the corrected Jason-2 VTEC; panel c is the STD

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4.2 The characteristics of COSMIC-JASON bias

The collocated observations of COSMIC and Jason are relatively limited due to the sparse distribution of occultation measurements. A climatological comparison of COSMIC/Jason-retrieved VTEC is conducted by calculating seasonal mean differences between these two observations. The seasons are represented by March equinox (‘ME’) (March, April and May), June solstice (‘JS’) (June, July and August), September equinox (‘SE’) (September, October and November) and December solstice (‘DS’) (January, February and December) in this study. Figures 8 and 9 illustrate the global distribution of VTEC residuals (COSMIC-Jason) for 2008 and 2014, respectively. The quarterly COSMIC and Jason TECs are averaged over each grid of 5° latitude and 10° longitude. The difference is determined by COSMIC grid mean value minus Jason’s. During the selected daytime periods (LT 12–16) in the LSA year (Fig. 8), the VTEC of COSMIC is evidently overestimated in the equatorial and mid-latitude areas, along with the magnetic inclination field lines. The crest-trough-like structures are identified in most seasons, which may be attributed to the retrieval errors of RO observations. When the equatorial ionization anomaly (EIA) is well developed around noon, the Abel retrieval method tends to overestimate the electron density to the north and south of the EIA crests (\(\pm 30^\circ\)~ \(\pm 50^\circ\)) and at the geomagnetic equator, while underestimates the electron density in the region surrounding the troughs (\(\pm 10^\circ\)~ \(\pm 30^\circ\)). This phenomenon results in three pseudo peaks and two depletions along the magnetic inclination lines (Wu et al. 2019; Yue et al. 2010). Moreover, the VTEC residuals demonstrate seasonal variations consistent with EIA evolution, presenting equinox asymmetry with larger crests and troughs in the spring equinox compared to the autumn equinox (Yue et al. 2015). During nighttime, the absolute differences decrease because the VTEC values are much lower than during daytime. In 2014, when the solar activity was more intensive, the VTEC difference increased with the growing strength of EIA crests and troughs according to Fig. 9. The equinox asymmetry is much more predominant, showing greater differences in the March equinox season than in the September equinox. During LT 0 ~ 4, the COSMIC VTEC is generally less than the Jason results between \(\pm 30^\circ\) of geomagnetic latitude. Particularly, the discrepancy of VTEC illustrates minor hemispheric asymmetry without obvious degradation in the ocean-dominant Southern Hemisphere. This also proves that with the compensation of topside TEC above 800 km, COSMIC VTEC shows good agreement with the Jason-1 and Jason-2 measurement under both LSA and HSA conditions. It indicates the feasibility of leveling the vertical range of different LEO satellites introduced by Eq. (6).

Fig. 8
figure 8

The mean difference between COSMIC and Jason-1 VTEC in 2008, LT 12–16 and LT 0–4. The white dashed and solid lines are magnetic inclination contour lines of the \(20^\circ\) interval

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Fig. 9
figure 9

Same as in Fig. 8 but for 2014. The corrected Jason-2 data are used

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4.3 The comparison among Jason, Sentinel and COSMIC VTEC

The comparison involving the Sentinel series was conducted in 2017, during which COSMIC-1 data were still available, although in lower volume. Given that Sentinel-3A shares similar orbit altitude with COSMIC, so no compensation was necessary when comparing these two datasets. Systematic bias was excluded by applying the calibration summarized in Eq. (7), which also corrected Jason-2 and Jason-3 TEC measurements accordingly. Consequently, all satellite altimetry ionospheric products were mapped into the relatively accurate frame of Jason-1 version ‘E.’ Figure 10 shows the histograms of each dataset compared to COSMIC VTEC during both daytime and nighttime. The colocation criterion was set at 2° of latitude, 6° of longitude and within 30 min. The criterion is slightly less strict than before to accommodate more matched observations for statistical analysis. According to Fig. 10, the agreement between COSMIC and Jason series is robust, with a correlation coefficient exceeding 0.9 during daytime. The mean biases of COSMIC and corrected Jason VTEC are 0.55 and 0.75 TECU, respectively, during daytime, and decrease to 0.27 and 0.25 TECU, respectively, at nighttime. The average difference between COSMIC and corrected Sentinel-3 TEC is about -0.5 TECU, with the STD being larger than the Jason comparison, especially at night. In conclusion, the mean bias and STD derived from collocated RO and SA VTEC measurements affirm the comparable accuracy of these two datasets.

Fig. 10
figure 10

The comparison of VTEC between COSMIC, Jason and Sentinel-3 in 2017. The corrected Jason and Sentinel results are used (denoted as ‘JASON2c,’ ‘JASON2c’ and ‘SENTINEL3c’)

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5 The global differences between COSMIC and GIM VTEC

Given that RO VTEC can be considered an accurate reference, we will now discuss the differences between COSMIC and GIM. A number of validation and evaluation studies have been performed since the launch in 2006. This section focuses on a detailed discussion of the ocean-land and hemispheric diversity in systematic bias between RO and ground-based GIM observations. The comparison is conducted during two distinct years, 2008 and 2014, to capture the scenarios of low and high solar activity. The daily mean and STD of the COSMIC-GIM VTEC difference are shown in Fig. 11. The COSMIC VTEC has been adjusted to the same vertical height of GIM VTEC. Notable seasonal variations are observed in both years, with higher STDs during the spring and autumn equinoxes, and smaller deviations during the solstice seasons. In 2008, the bias varies between -0.5 and 0.5 TECU, with minor day-to-day fluctuations. The daily F10.7 indexes are generally stable, except for a few instances of elevated values during the March equinox. The VTEC STD ranges between 1.0 and 2.5 TECU, with the lowest deviations during the June solstice season. As solar activities intensify in 2014, both the bias and STD increase significantly, especially during the equinox seasons. The seasonal variations in the VTEC difference are more predominant, with the STD occasionally ranging from 3 TECU to as high as 10 TECU. Moreover, the STD exhibits similar monthly periodical variations with the F10.7 index under high solar activity conditions, especially during the solstice seasons.

Fig. 11
figure 11

The seasonal variations in VTEC differences between COSMIC and GIM (\(VTEC_{RO}\)-GIM) in 2008 and 2014. The daily bias and STD are shown according to the left y-axis, and the F10.7 flux is plotted according to the right y-axis

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The ionospheric variations and physical characteristics across different latitudes are distinctive; therefore, we further investigated the latitude-dependent performances of RO VTEC with respect to GIM. According to Chen et al. (2020), the quality of GIM VTEC differs in the Southern and Northern Hemispheres at different latitudes, due to the influence of the marine and land distribution, as well as the density of GNSS tracking stations. The IGS combined maps are used since they are slightly better than any of the individual IAAC maps (Hernández-Pajares et al. 2009). The residuals between COSMIC and GIM are discussed in several geomagnetic latitude bands, \(- 15^\circ\)~\(15^\circ\), \(\pm 15^\circ\)~\(\pm 45^\circ\) and \(\pm 45^\circ\)~\(\pm 90^\circ\), representing low, mid- and high latitudes, respectively. Additionally, the surface types of oceans and land are separated in the statistics.

Figure 12 illustrates the bias and STD of the VTEC residual between COSMIC and GIM across different geomagnetic latitudes and local time periods in 2008. The difference between RO and GIM data is more noticeable at low and mid-latitude regions and less discernible at higher latitudes. Generally, the bias of the VTEC between \(- 15^\circ N\) and \(15^\circ N\) is below 1.5 TECU, while the STD ranges from 1 TECU to over 2.5 TECU, varying with local time. The absolute VTECs at equatorial areas are greater due to the enhanced solar radiation and the equatorial ionization anomaly. Diurnal variations are independent of latitude, with lower bias and STD observed during nighttime and higher values during daytime globally. Notably, disparities between the Northern and Southern Hemispheres are apparent, particularly in terms of VTEC bias, with residuals in mid-latitudinal areas escalating in the Southern Hemisphere. Given that the spaceborne technique is not constrained by the spatial–temporal distribution of measurements, the discrepancy between hemispheres may be attributed to the degradation in accuracy of GIM in the Southern Hemisphere, which is primarily ocean-dominated and experiences a significant reduction in ground-based stations. Generally, the STD of land areas is smaller than that of oceans. Figure 13 demonstrates similar findings but under high solar activity conditions. The equatorial STD increases to 8 TECU around noon and even higher at mid-latitudes. The VTEC residuals are smaller at high latitudes, especially in the Northern Hemisphere, with a bias less than − 1 TECU. The hemispheric asymmetry in accuracy is exacerbated, and the disparity in STD between ocean and land samples increases significantly, occasionally reaching 1 ~ 2 TECU during daytime.

Fig. 12
figure 12

The bias and STD of the VTEC residual between COSMIC and GIM at different geomagnetic latitudes and local time periods in 2008. The ‘Indian red’ and ‘dark blue’ bars represent the statistics over oceans and lands, respectively

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Fig. 13
figure 13

Same as in Fig. 12 but for 2014

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A summary is presented in Table 1 for the selected years 2008 and 2014, along with 2017, when Sentinel results are included. It compares the VTEC from collocated observations with same vertical coverage from RO, altimetry and GNSS data, calculating the mean bias and STD. \({\text{VTEC}}_{{{\text{RO}}}}^{\prime }\) and \({\text{VTEC}}_{{{\text{RO}}}}\) are defined in Eqs. (6) and (3), respectively. For GIM, analyses are conducted separately for the Northern and Southern Hemispheres. The absolute discrepancy between COSMIC and Jason is minimal, with the STD increasing from 1.7 TECU to approximately 5.2 TECU with higher solar activity level. The accuracy of GIM VTEC in the Northern Hemisphere is comparable to spaceborne results, while it degrades by approximately 0.7 TECU in 2008 and 1.7 TECU in 2014 in the Southern Hemisphere. The bias and STD of SA and RO data slightly increase in 2017. With appropriate calibration between different missions, SA and COSMIC ionospheric observations exhibit good agreement, as do the GNSS observations in the areas with dense tracking stations. However, GIM VTEC in the Southern Hemisphere is less reliable, necessitating the consideration of weights and variances in data combination and assimilation based on latitude.

Table 1 The statistics of VTEC differences among COSMIC, SA and IGS GIM (Unit: TECU)
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6 The ionospheric characteristics observed by different techniques

To investigate the ionospheric characteristics reflected by different observations, we analyzed the VTEC distributions of Jason, COSMIC and GIM during daytime periods (LT 12–16) in 2008, as well as in Fig. 15 for the year 2014. The four seasons are defined in the same way as in Sect. 4.2. According to the daytime TEC maps shown in Fig. 14, the EIA phenomenon (denoted as zone ‘A’)—symbolized by the northern and southern crests and equatorial trough structures lying along the geomagnetic latitudes—is most prominently observed in the Jason VTEC. The development of EIA demonstrates specific annual and semi-annual variations driven by the plasma composition variations (Qian et al. 2013), presenting stronger strength during equinoxes than solstices, and a hemispheric asymmetry, especially during solstice seasons. The March equinox of 2008 displays more pronounced EIA structures compared to the September equinox, with the northern summer asymmetry being more noticeable than the winter hemisphere. The crests in the northern hemisphere are more discernible across all maps during June solstices in both Figs. 14 and 15.

Fig. 14
figure 14

The global distribution of VTEC during LT 12–16 by Jason, COSMIC and GIM, respectively, in 2008. The white solid and dashed lines are magnetic inclination contour lines of interval \(20^\circ\); the thick black solid curves are the contour lines of zero magnetic declination

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Fig. 15
figure 15

Same as Fig. 14, but for 2014 during LT 12–16

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Figures 16 and 17 reveal more complicated ionospheric characteristics during nighttime periods (LT 0 ~ 4). Notably, the VTEC is suddenly enhanced at mid-latitudes around the southeastern Pacific Ocean and southwestern Atlantic Ocean (denoted as zone ‘B’ in Fig. 16). This phenomenon, popularly known as the Weddell Sea anomaly (WSA), is best demonstrated in the Jason and COSMIC VTEC maps in 2008. It is particularly prominent in longitude sectors where the dip equator shifts farthest toward the geographic pole. The spaceborne VTEC captures this structure in all seasons except for the June solstice under LSA conditions. Conversely, under HSA condition, the WSA is recognizable in the December solstice in all datasets but is barely visible in other seasons. The western boundary of the WSA is limited by contours of zero magnetic declination, depicted by thick black curves in the panels (Burns et al. 2008). While the COSMIC observations delineate the western boundary most accurately, the other two datasets exhibit some leakage beyond the magnetic declination line. Nevertheless, the GIM VTEC is less satisfactory in terms of describing these features due to the inadequate number of stations in the oceanic areas, especially in 2008.

Fig. 16
figure 16

Same as Fig. 14 but for 2008 during LT 0–4

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Fig. 17
figure 17

Same as Fig. 15 but for 2014 during LT 0–4

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In Fig. 16, the VTEC of GIM presents a striped enhancement at mid-latitude areas (denoted as zone ‘C’) along the magnetic inclination contour lines. This phenomenon, known as the mid-latitude electron density enhancement (MEDE), is less discernible in the COSMIC results and is mixed with the more pronounced WSA and MSNA in the Jason maps. As solar activity increases, the striped enhancement becomes barely visible in the satellite observations but remains detectable in the GIM VTEC, especially in the Pacific oceans (panel (c)-(l), Fig. 17). The longitudinal difference in MEDE is evident in 2008, characterized by distinct peaks and troughs to the north/south of the EIA structure in the Pacific Ocean and less strength between \(60^\circ W\) and \(90^\circ E\). The occurrence of MEDE is attributed to the \({\varvec{E}} \times {\varvec{B}}\) drift, neutral wind and ionosphere–plasmasphere plasma flow. Although Rajesh et al. (2016) proposed that the MEDE occurs at all times of the day and is even more frequent during daytime in some cases, we are not able to confirm its existence during LT 12–16 in this study based on the displayed TEC maps.

Another distinction between spaceborne and ground-based observations is the Wave Number Four (WN4) pattern (C. H. Lin et al. 2007). Longitudinal wave-like structures are prominent at night, as shown in Fig. 16 (the ‘D’ zone). There are stronger electron content peaks in EIA zones at South America, Africa and Southeast Asia regions. The COSMIC TEC maps outperform Jason in depicting this feature, benefitting from the average coverage of RO data. However, the GIM VTEC is disadvantageous in reflecting delicate longitudinal variations. During daytime, WN4 pattern is still discernable in Fig. 14 for Jason and COSMIC observations at low and mid-latitude regions but is hardly identified in the GIM VTEC maps.

In the mid-latitude areas of \(40^\circ\)~\(60^\circ\) (geomagnetic latitude), the wave-2/wave-1 longitudinal structure is predominant, especially in the Southern Hemisphere during both daytime and nighttime (denoted as zone ‘E’ in Figs. 15 and 17). In Fig. 15, the VTEC values in the southern longitude sector of \(45^\circ W\)~\(135^\circ E\) are significantly increased, while the left longitudes generally experience a decrease. In Fig. 17, the wave-like structure is totally antiphase with its daytime counterpart. The longitudinal west–east difference is intensified when the WSA occurs during the December solstice (panels (j)(k)(l)). Moreover, the longitudinal variations roughly coincide with changes in the magnetic declination sign, as indicated by the contours of zero declination. The phase of the wave-1 structure is opposite in the Northern and Southern Hemispheres and more prominent in the southern half and in HSA years. The possible mechanisms of the longitudinal variations in mid- and subauroral regions include thermospheric zonal winds, magnetic field geometry, pressure gradient, ion drag, viscous force and Coriolis force (Rajesh et al. 2016; Wang and Lühr 2016). For such large-scale longitudinal variation of ionosphere, GIM demonstrates comparable performance with SA and RO observations.

7 Conclusions

This study primarily investigates the differences among the RO-derived integrated VTEC, GIM VTEC and SA TEC measurements. COSMIC data were reprocessed by an improved Abel inversion method developed earlier to reduce the retrieval errors brought by spherical symmetric assumption. Comparisons were conducted for the years 2008 and 2014 to assess the impact of solar activities. The key findings are summarized as follows:

  1. (1)

    Systematic differences between Jason series and Sentinel-3 remain relatively stable across varying solar activity levels. Jason-1 VTEC serves as a standard reference, facilitating the mapping of other datasets into its frame through specific calibration for different data versions;

  2. (2)

    COSMIC and Jason VTEC exhibit good agreement with minor biases throughout the year. The STDs are approximately ~ 2 TECU and 5 TECU in 2008 and 2014, respectively. Discrepancy between SA and RO TEC increases during pronounced EIA structures at low latitudes, resulting from enhanced ionospheric horizontal gradients and degradation in RO retrieval. Jason and Sentinel series have comparable accuracy with COSMIC in 2017;

  3. (3)

    Deviations between compensated COSMIC and GIM VTEC demonstrate significant seasonal variations, with greater discrepancies during the spring and autumn equinoxes and reduced discrepancies during the solstices. STD ranges from 1.0 to 2.5 TECU in 2008 and increases dramatically to 3.0 ~ 10.0 TECU during periods of higher solar activities. GIM VTEC exhibits hemispheric asymmetry by latitude, indicating accuracy degradation in ocean-dominant regions;

  4. (4)

    EIA crests and troughs are well observed in Jason VTEC maps. Regional enhancements of WSA and longitudinal variations of WN4 in the ionosphere are better performed in Jason and COSMIC observations compared to GIM. COSMIC TEC maps outperform Jason in revealing the WN4 feature due to the even coverage of RO data over lands and oceans;

  5. (5)

    Spaceborne satellite measurements have advantages in reproducing delicate longitudinal features over the ground-based technique, except for MEDE, which is more pronounced in GIM. Wave-2/wave-1 structures are especially predominant in the Southern Hemisphere at mid-latitudinal and subauroral areas and are well represented well by all techniques.

The validation of multi-source ionospheric observations is fundamental for the combination and model construction from different datasets in the future work. Discrepancies among GNSS, radio occultation and SA satellite observations are associated with various factors, including the station locations, data retrieval errors, spatial and temporal variations and solar activity conditions. Our comprehensive investigation aimed to minimize intermission bias and establish systematic differences under the same vertical coverage. The good agreement observed among different datasets indicates the feasibility of leveling the vertical range between satellites using methods introduced in this study. This research could serve as a reference for determining observational covariance and weight matrices in data assimilation and ingestion studies.