## Data Presentation
### Calculation of the TEC and ROTI  
The ground GNSS observations are used to derive the TEC in the path between the GNSS satellite and a given receiver, and each satellite has slant TEC (STEC) according to its motion and coordinate related to the receiver. The ionosphere is considered a thin shell with a fixed height, where the TEC is concentrated and the absolute slant TEC can be produced to measure the status of the ionosphere at a given IPP. The proposed TEC calculation method is referred to as [PERSON] et al. (2007)'s arc-offset method [(29)] and realized by the software by the T/ICTD Lab of International Centre for Theoretical Physics. The detailed method is implemented as follows. For a given satellite and epoch, there are phases (\(\mathbf{L_{1}}\), \(\mathbf{L_{2}}\)) and the pseudo-ranges (\(\mathbf{P_{1}}\), \(\mathbf{P_{2}}\)) at the two dual carriers. Then, the following observation equations can be formed:  
\[P_{I}=P_{2}-P_{1}=STEC+b_{r,p}+b_{s,p}+\varepsilon_{p} \tag{1}\]  
\[L_{I,arc}=L_{1}-L_{2}=STEC+b_{r,l}+b_{s,l}+c_{arc}+\varepsilon_{l} \tag{2}\]  
where \(STEC\) denotes the slant TEC to be estimated; \(b_{r,p}\) and \(b_{s,p}\) denote the satellite and receiver code-delay inter-frequency biases (IFBs), with no ambiguity term; \(\varepsilon_{p}\) is the effect of noise and the multi-path for code-delay observations; \(\varepsilon_{l}\) is the effect of noise and the multi-path for carrier-phase observations ; \(b_{r,l}\) and \(b_{s,l}\) are the satellite and receiver IFBs for carrier-phase observations; and \(c_{arc}\) represents the bias produced by the carrier-phase ambiguities in the ionospheric observable. Assuming a constant IBF, taking the average of the subtraction between Equations (1) and (2), we get Equation (3)  
\[\left\langle L_{I,arc}-P_{I}\right\rangle_{arc}=c_{arc}+b_{r,l}-b_{r,p}+b_{s,l }-b_{s,p}-\left\langle\varepsilon_{p}\right\rangle_{arc} \tag{3}\]  
Note that Equation (3) neglects the noise and the multi-path on the carrier-phase observations \(\varepsilon_{l}\). By subtracting Equation (3) from Equation (2), the ambiguity term is removed from the carrier-phase ionospheric observable  
\[\widetilde{L}_{I,arc}=L_{I,arc}-\left\langle L_{I,arc}-P_{I}\right\rangle_{ arc}=STEC+b_{r,p}+b_{s,p}+\left\langle\varepsilon_{p}\right\rangle_{arc}+ \varepsilon_{l} \tag{4}\]  
Neglecting the noise term \(\varepsilon_{l}\), Equation (4) is further written by  
Figure 1: The locations of the Global Navigation Satellite System (GNSS) Multi-GNSS Experiment (MGEX) and the magnetometer sites selected by this work. \[\widetilde{L}_{I,arc,ijt}=STEC_{ijt}+b_{i,p}+b_{j,p}+\left\langle\varepsilon_{p} \right\rangle_{arc} \tag{5}\]  
This formula describes the slant TEC affected by the bias terms; \(i=1,2,\ldots,32+\) denotes available GNSS satellites; \(j=1,\ldots,\) denotes available receivers; \(t\) is all the available observation epochs (in one day or fraction, or many days). Arc is common to all continuous observations performed by receiver \(j\) on satellite \(i\) at times contiguous to \(\boldsymbol{t}\);\(\left\langle\varepsilon_{p}\right\rangle_{arc}\) is disregarded in the traditional approach but is basic for the alternative \"arc-offset\" solution. In [PERSON]'s method, the calibration is performed considering \(sTEC\) as functions of a set of unknown parameters \(1X1\), forming the residuals  
\[e_{ijt}=\widetilde{L}_{I,arc,ijt}-STEC_{ijt}(|X|)+b_{i,p}+b_{j,p}+\left\langle \varepsilon_{p}\right\rangle_{arc} \tag{6}\]  
with the least-squares estimation method, the parameters \(1X1\) and unknown biases \(\boldsymbol{b}_{i,p}\), \(\boldsymbol{b}_{j,p}\), \(\left\langle\varepsilon_{p}\right\rangle_{arc}\) can be estimated together. The overall procedures can be summarized as follows:  
1. Extraction of the un-calibrated slants from GNSS observations
2. Quality control of the GNSS observations, elevation mask, arcs discontinuities, recovery of cycle slips, and so forth. 3.