Modeling and Accuracy Evaluation of Ionospheric VTEC Across China Utilizing CMONOC GPS/GLONASS Observations

Abstract

Accurate estimation of the regional ionospheric model (RIM) is essential for Total electron content and high-precision applications of the Global Navigation Satellite System (GNSS). Utilizing dual-frequency observations from over 250 Crustal Movement Observation Network of China (CMONOC) monitoring stations, which are equipped with both GPS and GLONASS receivers, this study investigates the Vertical Total Electron Content (VTEC) estimation models over the China region and evaluates the estimation accuracy under both GPS-only and GPS+GLONASS configurations. Results indicate that, over the Chinese region, the spherical harmonic reginal ionospheric model (G_SH RIM) and polynomial function reginal ionospheric model (G_Poly RIM) based on single GPS observations demonstrate comparable accuracy with highly consistent spatiotemporal distribution characteristics, showing grid mean deviations of 1.60 TECu and 1.62 TECu, respectively. The combined GPS+GLONASS observation-based RIMs (GR_SH RIM and GR_Poly RIM) significantly improve the TEC modeling accuracy in the Chinese peripheral regions, though the overall average accuracy decreases compared to single-GPS models. Specifically, GR_SH RIM and GR_Poly RIM exhibit mean deviations of 2.15 TECu and 2.32 TECu, respectively. A preliminary analysis reveals that the reduced accuracy is primarily due to the systematic errors introduced by imprecise differential code biases (DCBs) of GLONASS satellites. These findings can provide valuable references for multi-GNSS regional ionospheric estimation.

1. Introduction

As an important part of the Earth’s upper atmosphere, ionospheric spatiotemporal evolution has a wide influence on GNSS signal transmission [1,2]. The rapid advancement of GNSS constellations, coupled with the exponential surge in GNSS observation data, has significantly amplified the demand for high-precision ionospheric modeling to achieve enhanced accuracy and superior positioning performance. It also plays an important role in advanced GNSS applications, spanning from space weather monitoring to high-precision remote sensing [3,4,5,6,7]. Traditional ionospheric models can be fundamentally categorized into two classes: (1) empirical models constructed from long-term observational datasets, such as the International Reference Ionosphere (IRI), NeQuik, and Klobuchar models [8,9,10], which provide well-parameterized climatological behaviors instead of dynamic evolution; and (2) mathematical models derived via parametric fitting of short-term ionospheric delay, exemplified by the Global Ionosphere Maps (GIMs) provided by the International GNSS Service (IGS) [11]. With the rapid development of GNSS constellations, global ionospheric modeling has emerged as a research frontier. Among them, the more famous ones are as follows: the global ionosphere model established by Mannucci and others using spherical triangle model [12]; Schaer using a spherical harmonic function model [13]; and Hernandez-Pajares and others using polynomial models [14]. However, for the existing GIMs, including the IGS GIMs, the uneven distribution of GNSS stations inherently limits the accuracy of Vertical Total Electron Content (VTEC) in data-scarce regions, where extrapolation or interpolation techniques often dominate data synthesis [15].

In recent decades, with the fast development of Multi-Mode and Multi-Frequency GNSS, satellite observation data have become more abundant and reliable, and numerous studies have explored global ionospheric modeling using GNSS combinations [16,17,18]. The Chinese region, which has a vast territory and complex terrain, has unique spatiotemporal variations in ionospheric activity that are significantly influenced by solar radiation and geomagnetic activity [19]. Meanwhile, the sparse distribution of IGS stations, compounded by data scarcity and accuracy inconsistencies, underscores the urgency of developing independent ionospheric monitoring capabilities. The Crustal Movement Observation Network of China (CMONOC) addresses this need with a nation-wide high-density GNSS continuous observation network [20,21], featuring denser station spacing and more uniform regional coverage, which enables fine-scale investigations of local ionospheric structures over China and its regions [22,23,24,25,26]. In the region of China and its adjacent areas, although some scholars have attempted new ionospheric assimilation technologies for ionospheric research [27,28], there has been no substantial progress in the modeling methods and accuracy evaluation for Multi-Mode and Multi-Frequency GNSS. So it is essential to investigate regional ionospheric models based on multi-GNSS observations to detect fine spatiotemporal ionospheric structure, and various efforts have illustrated that regional ionospheric modeling is still subjected to in-depth study, including the following: (1) quantifying the inversion accuracy of the VTEC following the integration of multi-GNSS observations over the China region; and (2) selecting region-adaptive models that align with local morphological characteristics.

In this work, a systematic investigation of ionospheric modeling tailored for the Chinese region is conducted by using more than 250 multi-GNSS observations from CMONOC, and integrating data from GPS and the Global Navigation Satellite System (GLONASS). The core objectives are twofold: (1) To characterize the spatiotemporal patterns of ionospheric VTEC inversion accuracy across China; and (2) to evaluate the impact of regional modeling strategies and heterogeneous observation configurations on the model performance. In the following, Section 2 briefly details the data and the methodology for constructing regional ionospheric models, while Section 3 validates the derived ionospheric grid models through rigorous comparisons with IGS GIM products. The implications of the findings are systematically discussed in Section 4. Finally, the research outcomes are succinctly summarized in the last section.

2. Data and Methods

2.1. Data

This study utilized observational datasets from over 250 CMONOC GNSS stations across China region during 1–7 January 2019 to develop a Regional Ionospheric Model (RIM). The modeling domain spanned longitudes 70° E to 140° E and latitudes 15° N to 55° N, with station distribution visualized in Figure 1. Different GNSS are denoted by distinct colored symbols, illustrating that the GNSS station spatial configuration exhibits higher density in eastern China compared to the western regions. This distribution epitomizes CMONOC’s strategic emphasis on tectonic monitoring while simultaneously safeguarding robust spatial sampling capabilities essential for ionospheric modeling.

Ionospheric pierce points (IPPs) serve as fundamental observable in ionospheric modeling. Figure 2 illustrates the spatial distribution of IPPs derived from GPS (red) and GLONASS (blue) observations during a 1 h interval (01:00–02:00 UT) on 1 January 2019. The figure demonstrates that IPPs from terrestrial network data afford dense coverage over China’s inland regions. However, pronounced IPP sparsity is evident in boundary zones, specifically within the 15° N latitude band across 70° E–90° E and 120° E–140° E longitude ranges, attributable to the absence of ground stations in oceanic areas. Given that terrestrial GNSS networks are predominantly deployed over continental landmasses, this sampling disparity inherently undermines the accuracy of ionospheric modeling in marginal regions.

2.2. Method Descriptions

This study introduces a comprehensive framework for modeling and evaluating RIMs over China, integrating GPS and GLONASS observations. The specific processes include four phases: (1) Theoretical derivation of RIM construction methodologies, focusing on different ionospheric parameterization model: spherical harmonic and polynomial function; (2) dual-frequency GPS VTEC RIM development: employing multi-epoch carrier-phase leveling and rigorous DCBs corrections using IGS reference products to calibrate the model; (3) quantitative spatiotemporal validation against IGS GIM: conducted via statistical analysis of RMS discrepancies and spatial correlation coefficients across a standardized 2.5° × 5° grid cell; and (4) receiver’s DCB stability characterization: utilizing standard deviation (STD) metrics to systematically quantify temporal variations in hardware-induced signal biases, contrasting stability profiles across modeling paradigms.

When GNSS signals propagate through the ionosphere, dual-frequency receivers enable accurate separation of the first-order ionospheric-induced delays by performing differential processing on signal delays at distinct frequencies, utilizing both pseudorange and carrier-phase. A widely adopted methodology is the phase-smoothed pseudorange algorithm [15,29,30,31], which capitalizes on the high-precision attributes of carrier-phase data and calibrates them with pseudorange measurements to derive the ionospheric Slant Total Electron Content (STEC) along the satellite-receiver propagation path; the calculation formula is expressed as follows [21,31]:

$$\begin{array}{cc}\mathrm{S}\mathrm{T}\mathrm{E}\mathrm{C}=-\hfill & {\displaystyle \frac{f_1^2{f}_2^2}{40.28\left(f_1^2{-f}_2^2\right)}}\left({\mathrm{P}}_{4,\mathrm{s}\mathrm{m}}-\mathrm{c}\times {\mathrm{D}\mathrm{C}\mathrm{B}}_{\mathrm{s}}-\mathrm{c}\times {\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}\right)\hfill \\ & =-{\displaystyle \frac{f_1^2{f}_2^2}{40.28(f_1^2{-f}_2^2)}}({\mathrm{P}}_{4,\mathrm{s}\mathrm{m}}^{\prime }-\mathrm{c}\times {\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}})\hfill \end{array}$$

(1)

Here, $f_1$ and $f_2$ represent the dual frequency bands of GNSS satellites, while ${\mathrm{P}}_{4,\mathrm{s}\mathrm{m}}$ denotes the code-leveled carrier phase ionospheric measurements for GPS and GLONASS, and ${\mathrm{P}}_{4,\mathrm{s}\mathrm{m}}^{\prime }$ refers to ${\mathrm{P}}_{4,\mathrm{s}\mathrm{m}}$ after considering ${\mathrm{D}\mathrm{C}\mathrm{B}}_{\mathrm{s}}$. The fundamental equation incorporates $\mathrm{c}$ (speed of light in vacuum) along with ${\mathrm{D}\mathrm{C}\mathrm{B}}_{\mathrm{s}}$ (satellite differential code bias) and ${\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}$ (receiver differential code bias), both measured in nanosecond (ns). Notably, DCB values for GNSS satellites and GNSS receivers generally remain stable throughout a 24 h period [18]. Therefore, STEC values are calibrated using IGS DCB products, after which the modified single-layer model (MSLM) converts STEC to VTEC through geometric mapping [31]:

$$\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}=\mathrm{c}\mathrm{o}\mathrm{s}(\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}({\displaystyle \frac{\mathrm{R}}{\mathrm{R}+{\mathrm{H}}_{\mathrm{i}\mathrm{o}\mathrm{n}}}}\mathrm{s}\mathrm{i}\mathrm{n}(\mathsf{\alpha }\mathrm{z})))\times \mathrm{S}\mathrm{T}\mathrm{E}\mathrm{C}$$

(2)

where z denotes the satellite elevation angle. $\mathrm{R}$ represents the Earth’s radius, and ${\mathrm{H}}_{\mathrm{i}\mathrm{o}\mathrm{n}}$ signifies the altitude of the ionospheric thin shell (adopting the CODE standard of 450 km). The coefficient $\mathsf{\alpha }$ = 0.978 is applied for STEC conversion.

2.3. Reginal Ionospheric Model over China

The ionosphere is usually simplified as a spherical thin shell in ground-based GNSS measurements due to the limited vertical resolution of such observations [31]. For the ionospheric modeling over the Chinese region, this study employs two simplified yet robust ionospheric modeling approaches: a Spherical Harmonic (SH) function model and a Polynomial (Poly) function model [31,32,33,34].

2.3.1. SH RIM

Considering the spatial coverage of our GNSS reference station network and the pronounced influence of solar and geomagnetic activity on the ionosphere, the SH function model is a well-established mathematical framework for ionospheric modeling [22,31,33,34], renowned for its robust structural basis that effectively captures both global-scale ionospheric variations and regional TEC features. This approach excels in transforming discrete GNSS-derived STEC into VTEC distributions via spherical harmonic expansions, offering distinct advantages in characterizing latitude-dependent ionospheric irregularities [7]. The VTEC SH model can be mathematically formulated as follows:

$$\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}(\mathsf{\beta },\mathrm{s})={\sum }_{\mathrm{n}=0}^{{\mathrm{n}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\sum }_{\mathrm{m}=0}^{\mathrm{n}}\left[{\tilde{\mathrm{P}}}_{\mathrm{n}\mathrm{m}}(\mathrm{s}\mathrm{i}\mathrm{n}\mathsf{\beta })({\mathrm{C}}_{\mathrm{n}\mathrm{m}}\cos (\mathrm{m}\mathrm{s})+{\mathrm{S}}_{\mathrm{nm}}\sin (\mathrm{m}\mathrm{s}))\right]$$

(3)

In this context, $\mathsf{\beta }$ denotes the geocentric latitude of IPPs, while $\mathrm{s}$ corresponds to the solar-fixed longitude of IPPs. The parameter n represents the degree of the spherical harmonic function (with ${\mathrm{n}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$= 6 in this study), and m signifies the order of the spherical harmonic function. Here, ${\tilde{\mathrm{P}}}_{\mathrm{n}\mathrm{m}}$ stands for the regularized Legendre series of degree n and order m, whereas ${\mathrm{C}}_{\mathrm{n}\mathrm{m}}$ and ${\mathrm{S}}_{\mathrm{n}\mathrm{m}}$ denote the spherical harmonic coefficients to be calculated.

Substituting Equations (1) and (2) into Equation (3) yields the following:

$$\begin{gathered} \mathrm{c}\mathrm{o}\mathrm{s}(\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}({\displaystyle \frac{\mathrm{R}}{\mathrm{R}+{\mathrm{H}}_{\mathrm{i}\mathrm{o}\mathrm{n}}}}\mathrm{s}\mathrm{i}\mathrm{n}(\mathsf{\alpha }\mathrm{z})))\left[-{\displaystyle \frac{f_1^2{f}_2^2}{40.3(f_1^2-f_2^2)}}({\mathrm{P}}_{4,\mathrm{s}\mathrm{m}}^{\prime }-\mathrm{c}\times {\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}})\right] \\ ={\sum }_{\mathrm{n}=0}^{{\mathrm{n}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\sum }_{\mathrm{m}=0}^{\mathrm{n}}\left[{\tilde{\mathrm{P}}}_{\mathrm{n}\mathrm{m}}(\mathrm{s}\mathrm{i}\mathrm{n}\mathsf{\beta })({\mathrm{C}}_{\mathrm{n}\mathrm{m}}\cos (\mathrm{m}\mathrm{s})+{\mathrm{S}}_{\mathrm{nm}}\sin (\mathrm{m}\mathrm{s}))\right] \end{gathered}$$

(4)

2.3.2. Poly RIM

The polynomial function model, distinguished by its parsimonious structure and robust fitting capability over small-scale regions, is widely employed in regional ionospheric modeling [31,33]. The mathematical formulation of this model is expressed as follows:

$$\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}(\mathsf{\beta },\mathrm{s})={\sum }_{\mathrm{i}=0}^{\mathrm{n}}{\sum }_{\mathrm{j}=0}^{\mathrm{m}}{\mathrm{E}}_{\mathrm{i}\mathrm{j}}{(\mathsf{\beta }-{\mathsf{\beta }}_0)}^{\mathrm{i}}{(\mathrm{S}-{\mathrm{S}}_0)}^{\mathrm{j}}$$

(5)

In the formula, n and m correspond to the order and degree of the polynomial model, respectively. ${\mathrm{E}}_{\mathrm{i}\mathrm{j}}$ signifies the coefficients to be determined. Here, $\mathsf{\beta }$ and $\mathrm{S}$ denote the geographic latitude and solar hour angle of the IPPs, while ${\mathsf{\beta }}_0$ and ${\mathrm{S}}_0$ represent the latitude and solar hour angle of the regional center point at the computation epoch.

Substituting Equations (1) and (2) into Equation (5) yields the following expression:

$$\begin{gathered} \mathrm{c}\mathrm{o}\mathrm{s}(\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}({\displaystyle \frac{\mathrm{R}}{\mathrm{R}+{\mathrm{H}}_{\mathrm{i}\mathrm{o}\mathrm{n}}}}\mathrm{s}\mathrm{i}\mathrm{n}(\mathsf{\alpha }\mathrm{z})))\left[-{\displaystyle \frac{f_1^2{f}_2^2}{40.3(f_1^2-f_2^2)}}({\mathrm{P}}_{4,\mathrm{s}\mathrm{m}}^{\prime }-\mathrm{c}\times {\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}})\right] \\ ={\sum }_{\mathrm{i}=0}^{\mathrm{n}}{\sum }_{\mathrm{j}=0}^{\mathrm{n}}{\mathrm{E}}_{\mathrm{i}\mathrm{j}}{(\mathsf{\beta }-{\mathsf{\beta }}_0)}^{\mathrm{i}}{(\mathrm{S}-{\mathrm{S}}_0)}^{\mathrm{j}} \end{gathered}$$

(6)

Each hour’s observations are gathered and structured into a comprehensive system of linear equations:

$$\left\{\begin{array}{c}\underset{n\times m}{A}\cdot \underset{m\times 1}{X}=\underset{n\times 1}{L}\\ m={(order+1)}^2+m_r\end{array}\right.$$

(7)

where X denotes the unknown parameter vector of the model to be solved, composed of ${\mathrm{C}}_{\mathrm{n}\mathrm{m}}$, ${\mathrm{S}}_{\mathrm{n}\mathrm{m}}$, and ${\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}$ (or ${\mathrm{E}}_{\mathrm{i}\mathrm{j}}$ and ${\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}$). A represents the coefficient (design) matrix, and L signifies the observation vector. The X including ${\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}$ of GPS and/or GLONASS can be estimated using the weighted least squares method [21,34]:

$$\mathrm{X}={({\mathrm{A}}^{\mathrm{T}}\mathrm{P}\mathrm{A})}^{-1}{\mathrm{A}}^{\mathrm{T}}\mathrm{P}\mathrm{L}$$

(8)

Here, P is the weight determined according to the observed altitude angle. Figure 3 depicts the specific flowchart of ionospheric RIM calculation based on the ground-based GNSS observations. The detailed parameter settings involved in different RIMs are shown in

Table 1. Configuration parameters of different RIMs over China.

RIM	G_SH	GR_SH	G_Poly	GR_Poly
Observation	GPS	GPS+GLONASS	GPS	GPS+GLONASS
Data type	Phase smoothing pseudo-range	Phase smooth pseudo-range	Phase smooth pseudo-range	Phase smooth pseudo-range
Sampling rate	30 s	30 s	30 s	30 s
Cutoff angle	20°	20°	20°	20°
Earth radius	6371 km	6371 km	6371 km	6371 km
MF function	MSLM	MSLM	MSLM	MSLM
VTEC model	SH function	SH function	Poly function	Poly function
Spatiotemporal resolution	5° × 2.5° × 1 h	5° × 2.5° × 1 h	5° × 2.5° × 1 h	5° × 2.5° × 1 h
Modeling results	RIM + ${\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}$	RIM + ${\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}$	RIM + ${\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}$	RIM + ${\mathrm{D}\mathrm{C}\mathrm{B}}^{\mathrm{r}}$

.

2.4. Accuracy Evaluation Method

Assessing the accuracy of RIM in both internal and real-world applications remains crucial [35]. Given that ionospheric VTEC cannot establish a definitive truth value [36,37], we first evaluate the internal coincidence accuracy of the RIMs through the Root Mean Square (RMS) calculations across China to illuminate its spatiotemporal precision distribution. The RMS, serving as a key metric, is expressed as follows:

$$\mathrm{R}\mathrm{M}\mathrm{S}=\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{M}}{\left({\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}}_{\mathrm{R}\mathrm{I}\mathrm{M}}^{\mathrm{i}}-{\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}}_{\mathrm{o}\mathrm{b}\mathrm{s}}^{\mathrm{i}}\right)}^2/\mathrm{M}}$$

(9)

Here, M denotes the number of epochs, while ${\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}}_{\mathrm{R}\mathrm{I}\mathrm{M}}^{\mathrm{i}}$ represents the RIM VTEC value at each grid point, rigorously compared against the ionospheric VTEC value derived from dual-frequency GNSS observations. Meanwhile, to evaluate the external precision of distinct RIMs, the IGS GIMs were utilized as the reference. A thorough statistical assessment of both systematic biases and stochastic variations was performed, involving point-by-point analysis of mean residuals and their corresponding standard deviations across all grid points [35,37,38,39,40]. The bias and STD are presented as follows:

$$\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}={\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left({\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}}_{\mathrm{R}\mathrm{I}\mathrm{M}}^{\mathrm{i}}-{\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}}_{\mathrm{G}\mathrm{I}\mathrm{M}}^{\mathrm{i}}\right)/\mathrm{N}$$

(10)

$$\mathrm{S}\mathrm{T}\mathrm{D}=\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}}_{\mathrm{R}\mathrm{I}\mathrm{M}}^{\mathrm{i}}-{\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}}_{\mathrm{G}\mathrm{I}\mathrm{M}}^{\mathrm{i}}-\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}\right)}^2/\mathrm{N}}$$

(11)

where N is the number of each spatial grid, and ${\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}}_{\mathrm{G}\mathrm{I}\mathrm{M}}^{\mathrm{i}}$ represents the GIM VTEC value at each grid point.

3. Results

3.1. Accuracy Assessment of Inner Coincidence

Based on the methodologies described above, GPS and GLONASS observation datasets were utilized to derive ionospheric VTEC maps over the China region. First of all, we presented the RMS distribution for different inversion scenarios. As an instance, Figure 4 depicts the spatial distribution of RMS at 08:00 UT from 1 to 7 January 2019, obtained through various inversion methods. Specifically, (a) represents GPS inversion results based on spherical harmonics; (b) shows GPS+GLONASS inversion results using spherical harmonics; (c) denotes GPS inversion results based on polynomial functions; and (d) represents GPS+GLONASS inversion results using polynomial functions. As illustrated in Figure 4, the morphological distributions of (a) and (c), as well as (b) and (d), exhibit substantial consistency. For most areas over the Chinese region, the RMS values generally remain within 1 TECu (Total Electron Content Units, 1 TECu = 10¹⁶ electrons/m²), with the exception of the northwest and southwest regions. This suggests that, for the Chinese region, the accuracy of RIM using either spherical harmonics or polynomial functions is comparable, whether relying solely on GPS or combining GPS and GLONASS observations. Comparative assessment of Figure 4a vs. Figure 4b and Figure 4c vs. Figure 4d demonstrates discernible reductions in RMS values across specific regions (e.g., southwestern and northwestern domains). Specifically, joint inversion of GPS and GLONASS data yields significantly improved ionospheric VTEC accuracy in China’s border regions compared to GPS-only inversion. A plausible explanation for this observation is the enhanced spatial density of IPPs in boundary areas, facilitated by the inclusion of GLONASS observations. This augmented IPP distribution mitigates sampling gaps and improves spatial resolution; thus, the inversion accuracy of the geographically complex boundary areas has been improved.

3.2. Evaluation of Exterior Coincidence Accuracy

The RMS of the above-mentioned statistics merely reflects the internal conformity accuracy of ionospheric VTEC inversion. In order to further validate the accuracy of the RIM estimated in this paper, the IGS GIM are employed as the reference framework to evaluate the average bias and STD differences between various RIMs and GIM. Figure 5 presents the bias statistics and fitting outcomes of different RIMs versus IGS GIM for 1 January 2019. In this figure, (a), (b), (c) and (d), respectively, represent the error statistics and fitting results between G_SH, GR_SH, G_Poly, GR_Poly RIM, and IGS GIM. For each subgraph, the upper part shows the error statistics between RIM and GIM, presenting their bias and STD; the lower part displays the fitting situation between the two, providing their fitting form and correlation coefficient. When utilizing GPS data exclusively, the SH-based G_SH RIM and Poly-based G_Poly RIM exhibit average biases of −1.59 TECu and −1.47 TECu relative to GIM, accompanied by STDs of 2.02 TECu and 2.76 TECu, respectively. The integration of GPS and GLONASS observations reveals that the GR_SH RIM maintains comparable bias levels to G_SH RIM while demonstrating moderate improvement in STD. Comparative analysis of Figure 5c,d highlights enhanced alignment between the GR_Poly RIM and GIM, particularly evident in the 20–25 TECu range where VTEC data dispersion decreases substantially. While the GR_Poly RIM shows a 0.42 TECu bias increase than G_Poly RIM, it achieves a remarkable STD reduction from 2.76 TECu to 1.62 TECu alongside a correlation coefficient improvement from 0.70 to 0.87. Relative to GR_SH RIM, GR_Poly RIM demonstrates 0.25 TECu STD reduction despite a 0.29 TECu bias increment, with both models achieving robust correlation coefficients of 0.85 and 0.87, respectively.

To comprehensively evaluate the accuracy of regional ionospheric VTEC inversion in China, this paper statistically analyzes the spatial distribution of differences between inversion results from different models (RIMs) and IGS GIM. Figure 6 presents the spatial distribution of mean residuals for each RIM relative to GIM (with a 4 h interval due to space constraints) from 1 to 7 January 2019: (a) G_SH RIM, (b) GR_SH RIM, (c) G_Poly RIM, and (d) GR_Poly RIM. The results show that the average differences in most regions generally do not exceed 2 TECu, with larger discrepancies primarily distributed along regional boundaries, particularly in northwestern, southwestern, and low-latitude southern China. Comparing (a) (b) with (c) (d) reveals that, in boundary regions like the southwest and northwest, GR_SH RIM and GR_Poly RIM exhibit significantly smaller deviations from GIM than G_SH RIM and G_Poly RIM. However, in southeastern regions with dense GLONASS IPPs, their deviations from GIM increase instead, especially at 04:00 UT and 16:00 UT; this occurs because GPS IPPs are sparsely distributed in eastern and southeastern China, and incorporating GLONASS observations substantially increases IPPs, thereby objectively amplifying GIM deviations. In conclusion, G_SH RIM and G_Poly RIM, which rely solely on GPS observations, show minor differences in inversion accuracy across China, though both exhibit notable boundary effects. By contrast, after integrating GLONASS data, GR_SH RIM and GR_Poly RIM improve inversion accuracy in boundary regions but, respectively, experience an accuracy reduction of 0.60% and 28.50%.

To quantitatively evaluate the accuracy of differences in ionospheric RIMs inverted by different models relative to the IGS GIM, this study presents the statistical distribution characteristics of deviations for various RIMs over 24 observation periods from 1 to 7 January 2019 in Figure 7. The statistical results demonstrate that, in most observation periods, the G_SH RIM and G_Poly RIM ionospheric products, computed based on single GPS observation data, exhibit comparable accuracy levels. Notably, during the 07:00 UT period, the deviation value of the G_SH model is 8.00% higher than that of the G_Poly RIM. After adopting combined GPS+GLONASS observations, the average bias of both GR_SH RIM and GR_Poly RIM relative to GIM increased, with RIM STD exhibiting phased differences manifested as an increase by 1.07% and 2.79% during 08:00–14:00 UT for the combined solution, while the STDs of the combined solution during 15:00–24:00 UT are 31.21% and 27.34% smaller than that of the single GPS observation solution. This phenomenon aligns with the previously proposed conclusion that VTEC retrieval differences exhibit local time dependence [41], and the increased bias may be related to enhanced ionospheric gradients caused by solar radiation.

Table 2. Statistical results of the VTEC difference between RIMs and the IGS GIM (Unit: TECu).

RIM	G_SH		GR_SH		G_Poly		GR_Poly
Statistic	Bias	STD	Bias	STD	Bias	STD	Bias	STD
1 January	−1.59	2.02	−1.60	1.87	−1.47	2.76	−1.89	1.62
2 January	−1.19	1.66	−1.33	1.62	−1.39	1.88	−1.64	1.82
3 January	−1.58	1.83	−1.95	1.43	−1.74	1.68	−2.11	1.61
4 January	−1.60	2.05	−1.99	1.94	−1.55	1.88	−2.65	1.83
5 January	−2.16	2.14	−2.93	2.26	−2.12	2.08	−2.86	1.88
6 January	−1.63	1.92	−2.83	1.88	−1.56	2.16	−2.67	1.61
7 January	−1.42	2.08	−2.27	2.17	−1.47	2.24	−2.40	2.10
Mean	−1.60	1.96	−2.15	1.90	−1.62	2.10	−2.32	1.78

presents the statistical results of the average bias and STD of RIM relative to GIM calculated based on different models and observations from 1 to 7 January 2019. Through the analysis of Table 2, the following can be obtained: Based on single GPS observations, the accuracy of G_SH RIM reconstructed by SH function is comparable to that of G_Poly RIM reconstructed by Poly function, with the average bias being −1.60 TECu and −1.62 TECu, respectively; compared with single GPS observations, the average bias of RIM calculated by combining GPS and GLONASS increases, and the GR_SH RIM and GR_Poly RIM increase by 0.55 TECu and 0.70 TECu, respectively; when combining GPS+GLONASS observations, the STD of deviation between GR_SH RIM based on spherical harmonic function and GIM changes little, being 1.96 TECu and 1.90 TECu, respectively. However, the average STD of GR_Poly RIM relative to GIM decreases significantly from the original 2.10 TECu to 1.78 TECu.

3.3. Accuracy Evaluation of Receiver DCBs Estimation

Generally, the DCB of a receiver remains stable for a short period of time [18]. As code bias parameters and ionospheric VTEC parameters are coupled within the observation equations, the accuracy of VTEC modeling depends significantly on both DCB estimation precision and its inherent stability [42,43]. The reliability of DCB values directly mirrors the inversion accuracy of ionospheric VTEC. To assess the stability of the estimated DCBs, Figure 8 illustrates the seven-day average STD distribution of DCBs for GPS and GLONASS receivers from 1 to 7 January 2019. In the upper panel, the figure illustrates the GPS receiver DCB results, while the lower panel depicts the DCBs for the GLONASS receivers. For single GPS observations, the Poly model exhibits greater variability in estimated receiver DCBs compared to the G_SH model, with average STD values of 1.20 ns and 1.91 ns. Following the incorporation of GLONASS data, both models demonstrate notably reduced volatility in DCB estimates, with the discrepancy between their fluctuations diminishing, and with averages of STDs being 1.23 ns and 1.22 ns, respectively; regarding DCBs for the GLONASS receivers, the GR_Poly RIM demonstrates superior performance over the GR_SH RIM, with average STDs being 3.42 ns and 2.84 ns, respectively. This finding aligns closely with VTEC estimation accuracy trends. At the same time, we can find from Figure 8 that the receiver DCBs of some stations have a higher STD compared to other observation stations, regardless of the model used, due to the quality of the observed data. Overall, for the estimation results of GPS receiver DCB, when using GPS observations alone, G_Poly RIM is inferior to G_SH RIM, while, when combined with GPS and GLONASS observations, the volatilities of GPS receiver DCBs for both are basically equivalent, which is consistent with the morphological distribution of STD in Table 2 regarding VTEC estimation results. Whether using spherical harmonics or polynomial function models, the estimated GLONASS receiver DCBs exhibit greater volatility compared to the DCB estimation for GPS receiver.

4. Discussion

High-precision modeling of ionospheric VTEC is of great significance, and with the fast development of multi-constellation and multi-frequency GNSS (including GPS, BDS, GLONASS, and so on) [44,45], more and more research on the modeling and monitoring of global ionospheric VTEC have begun to be carried out [4,21,22,46,47]. Although existing studies have been dedicated to establishing accurate GIM/RIM products and validating their performance through actual measurements, there is still a need for a RIM with higher spatiotemporal resolution for certain regions (such as China and its neighboring areas). In particular, whether and how the accuracy of RIMs can be improved based on multi-mode GNSS observations is worth exploring.

In this paper, the regional ionospheric modeling over China from 1 to 7 January 2019 has been investigated and evaluated. Compared with the Chinese RIMs derived from single GPS observations, the ionospheric RIMs inverted through combined GPS and GLONASS data fail to deliver a marked enhancement in accuracy except within boundary zones characterized by sparse or absent IPPs. The performance of the GNSS TEC inversion model is closely tied to ionospheric conditions. This study specifically examines inversion accuracy during ionospheric quiet periods. Single mode can obtain better results, and the advantages of multi-mode cannot be reproduced, which may lead to the misjudgment of the actual performance of the model. In order to further investigate the inversion accuracy of different modeling methods in different spatial environments, the sample size of 7 days is far from enough. Random errors (such as observation noise and receiver deviation) may significantly affect the estimation of model parameters, resulting in the lack of universality of the calibrated model. Under magnetic disturbance conditions, the dual-mode system can significantly improve the inversion accuracy because of the large number of satellites and strong orbital complementarity, which can make up for the loss of single-mode data.

This phenomenon stems from two primary factors: for one thing, this is because the reference data used in this paper is IGS GIM. As we know, there are only few IGS observation stations within the research area of this paper, and the accuracy of IGS GIM in the Chinese region is only 3–8 TECu. Therefore, the accuracy evaluation presented in this paper can only be regarded as a preliminary research result and may not fully represent the real situation; for another, the ionospheric modeling scope in this study spans 15–55° latitude and 70–140° longitude. Despite integrating GLONASS observations, the ionospheric piercing points remain exceptionally scarce at the periphery of this domain, as shown in Figure 2. Particularly in southwestern and northwestern sectors, where over 250 GNSS observations still prove insufficient for GLONASS to substantially elevate RIM precision. Meanwhile, in low-latitude regions such as southwest and south China, the ionosphere undergoes drastic changes, with equatorial ionospheric anomalies existing. Strong longitude gradients (e.g., near 110° E) lead to the fragmentation of the VTEC spatial structure, causing the failure of the traditional single-layer model assumptions [48]; in addition, dual-frequency GNSS technology relies on the signal delays to resolve VTEC. Unlike GPS, GLONASS employs frequency division multiple access technology, assigning distinct frequency bands to individual satellites. This inherent signal disparity amplifies error propagation during joint data processing, ultimately compromising VTEC inversion fidelity. The DCBs of receivers and satellites are difficult to fully calibrate, even during relatively quiet geomagnetic conditions, leading to an inversion error of approximately 2 TECu. To advance the accuracy of the ionospheric VTEC modeling over the Chinese region via multi-GNSS integration, future efforts should prioritize two crucial pathways: implementing adaptive weighted fusion strategies, such as enhancing data processing capabilities, dynamically calibrating observation weights based on signal-to-noise ratios, and refining multi-frequency hardware delay compensation algorithms for unlocking higher inversion precision.

5. Conclusions

In this investigation, utilizing GNSS observations from more than 250 COMONC stations, we have precisely mapped VTEC across the Chinese region and conducted an exhaustive statistical evaluation of its precision. The principal insights gleaned from our investigation are outlined below:

(1)

Employing single GPS observations, G_SH RIM and G_Poly RIM exhibit comparable accuracy, demonstrating negligible discrepancies in their bias and STD values. Both models maintain an average bias relative to IGS GIM confined within 2 TECu, while more pronounced deviations are predominantly concentrated along geographical boundaries such as China’s northwestern and southwestern regions.

(2)

For GR_SH RIM, integrating GPS and GLONASS observations, both the average bias and STD compared to GIM exhibit a marked increase. Similarly, the average bias of GR_Poly RIM relative to IGS GIM also rises, while its average STD undergoes a notable reduction.

(3)

The G_SH RIM, when calculating the DCBs of GPS receivers using single GPS observations, demonstrates superior stability compared to the G_Poly RIM. Incorporating GLONASS observations exerts minimal impact on the DCBs of GPS resolved by the SH function, whereas for the Poly model, combined observations substantially diminish the STD of DCBs for both GPS and GLONASS receivers.

The results quantify the accuracy of different RIMs over the China region. However, this study only provides preliminary evaluation and analysis during magnetically quiet periods; the next step is to investigate the inversion accuracy in different solar-terrestrial space environments and the mechanisms behind it.