# Performance Evaluation of VTEC GIMs for Regional Applications during Different Solar Activity Periods, Using RING TEC Values

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## Abstract

**:**

## 1. Introduction

## 2. Determination of TEC Using GIMs Interpolation and Ciraolo Method

_{GIM}) and the Ciraolo et al. [17] method (corresponding values are hereafter identified as TEC

_{CIR}). Then, values calculated at the same grid points through both methods have been compared for the following three periods:

- from July 2008 to June 2009, a period of LSA with an average value of the solar index R
_{12}= 3.1, where R_{12}is the 12 month running mean of the monthly sunspot number; - from September 2013 to August 2014, a period of HSA with an average value of R
_{12}= 110.6; - March 2015, including the St. Patrick storm occurred on 17–19 March characterized by a maximum value of the geomagnetic index K
_{p}= 8, where K_{p}is a 3 h geomagnetic index (whose maximum value can be 9) that aims at describing the global level of all irregular disturbances of the geomagnetic field.

_{p}< 3

^{+}are considered as a “quiet dataset”, while data characterized by a K

_{p}≥ 3

^{+}are considered as a “disturbed dataset”.

#### 2.1. The GIMs Interpolation

#### 2.2. Single Station TEC Determination by Ciraolo Method

^{16}electrons/m

^{2}), I is the equivalent ionospheric range delay (time delay converted in length unit), and α is a conversion factor to obtain length units from TECU. The subtraction of simultaneous carrier phase observations at different frequencies leads to an observable in which all frequency-independent effects (e.g., the satellite receiver geometrical range, clock errors, tropospheric delay, etc.) are cancelled, except the ionospheric and any other frequency-dependent effects. This is the so-called “geometry free linear combination” represented as

_{R}and b

_{S}are the corresponding IFBs, often called differential code biases (DCBs), due to the transmitting and the receiving hardware, and ${\epsilon}_{\mathrm{P}}$ is the noise on code measurements. Subtracting the two new observables (one for code measurements and the other one for phase measurements) for every continuous arc of observations, one can obtain the average difference between code carrier phase and code observables along a single arc:

_{arc}is the arc-offset, a constant to be determined for each arc of observation related to a given receiver and satellite pair. β

_{arc}represents the contribution of receiver and satellite biases (b

_{R}+ b

_{S}), and the contribution of any nonzero averaged errors over an arc of observation and of the multipath. Equation (8) is the basic relation used to calibrate the total electron content. To accomplish this task, sTEC values are mapped as a two-dimensional (2D) surface by means of the classical thin shell method as

_{n}is the term of the polynomial and c

_{n}the corresponding coefficient. The relationship (10) is linear in the unknown coefficients c

_{n}and phase offsets β

_{arc}, and so it can be solved via standard least-squares method.

_{CIR}time series. Hence, to be consistent with the 2 h time resolution of GIMs, for each day of the three selected periods, values corresponding at 00, 02, …, 20, 22 universal time (UT) have been considered.

## 3. Results and Discussion

_{GIM}vs. TEC

_{CIR}) for STUE, INGR, and RESU are shown for LSA and HSA periods in Figure 1 and Figure 2, respectively, distinguishing also between quiet (K

_{p}< 3

^{+}) and disturbed (K

_{p}≥ 3

^{+}) geomagnetic datasets. Of course, the number of values related to disturbed conditions is much lower than the one characterizing quiet conditions because, usually, the number of geomagnetically disturbed days is by far lower than quiet ones. The number N of TEC values used in the study is shown inside each plot for all datasets.

_{GIM}values are always higher than TEC

_{CIR}values, independently of solar activity, geomagnetic conditions and latitude, even though the correlation between the two datasets is really good (≥0.9) for all conditions, as it will be shown at the end of this section. This could be due to the different assumptions made for the DCBs estimation by IGS and Ciraolo algorithm. In fact, GIMs are calculated by forcing to zero the sum of all the satellites DCBs, while the Ciraolo algorithm assumes that β (see Equation (10)) is constant over each arc of observation. Moreover, Figure 1 and Figure 2 show that the difference between TEC

_{GIM}and TEC

_{CIR}values presents a latitudinal dependence; the intercept of the linear regression in fact shows that this difference increases from the north to the south of Italy. This issue is consistent with previous studies by Jee et al. [14] and Abe et al. [17], who found that TEC

_{GIM}estimates are more reliable at mid-latitudes than at low latitudes, where the dynamics of the ionospheric plasma is much more complex to be modeled.

_{GIM}–TEC

_{CIR}) with the corresponding standard deviation. Corresponding analyses are based on a joined HSA and LSA dataset and on averages of all values obtained respectively at 00, 02, …, 20, 22 UT (Figure 3), and for each month (Figure 4). Figure 5, Figure 6, Figure 7 and Figure 8 report the same analyses shown in Figure 3 and Figure 4 but considering the LSA and HSA dataset separately.

_{GIM}–TEC

_{CIR}) increases as the solar activity increases, confirming what was previously found by Jee et al. [14], who suggested a mismodeling of the plasmaspheric contribution by GIMs for high solar activity. Mean daily variation of the difference (TEC

_{GIM}–TEC

_{CIR}) is characterized by a maximum, which is reached at around 14 UT (see Figure 3); this feature is still visible when distinguishing between LSA and HSA (see Figure 5 and Figure 7). However, one would expect to obtain larger differences around solar terminator hours—when large electron density gradients take place—than around noon, when the ionospheric plasma can be considered almost stationary [32]. This might occur due to a GIMs mismodeling of a mid-latitude phenomenon known as meridian depression. The meridian depression is a peculiarity for which the daily absolute maximum of electron density is observed a few hours past the local noon; it has been recently renamed as Mid latitude Summer Evening Anomaly (MSEA) [33]. The main possible mechanism considered at the base of the meridian depression is the variation of the ratio [O]/[N

_{2}], which increases from noon to midnight. Due to the longitudinal gradients of the [O]/[N

_{2}] ratio, consistent longitudinal-dependent variations in the meridian depression magnitude may occur. This might represent mostly a problem for GIM’s generation that is based on global interpolation and less for the single site calibration method developed by Ciraolo et al. [17].

_{GIM}and TEC

_{CIR}are significantly affected by geomagnetically disturbed conditions. In fact, independently of solar activity, season, hour of the day, and latitude, the difference (TEC

_{GIM}- TEC

_{CIR}) increases for values of the geomagnetic index K

_{p}≥ 3

^{+}; this means that, for geomagnetic disturbed conditions, the method (either global or local) used to estimate TEC values has to be carefully selected.

_{GIM}vs. TEC

_{CIR}) and corresponding residuals (TEC

_{GIM}–TEC

_{CIR}) for the whole month of March 2015, which includes the well-known St. Patrick storm that occurred between 17 and 19 March 2015. Scatterplots are in line with those of Figure 2 obtained for HSA and disturbed conditions, but the most significant features shown by Figure 9 are the very large differences characterizing the March 17, as soon as the geomagnetic storm starts. During abrupt and strong geomagnetic variations, the GPS data processing is quite complicated. Specifically, in these conditions, the much more probable presence of ionospheric irregularities causes a higher number of cycle slips in carrier phases, which are difficult to be managed (e.g., Zhang et al. [36]). Therefore, during extreme geomagnetic conditions, it is hard to assess which method is the most suitable to be used.

_{GIM}–TEC

_{CIR}) for the considered stations, under different solar and geomagnetic conditions, Figure 10 reports the Taylor diagram [37] for all the analyzed datasets. In this diagram, the y-axis represents the TEC

_{GIM}standard deviation (SD) normalized to the TEC

_{CIR}standard deviation (SD

_{CIR}), the x-axis represents the normalized (or centered) root mean square error (NRMSE), and the circular axis represents the correlation coefficient R. This diagram has the peculiarity to represent three parameters in a two-dimensional plot, according to the following relation:

_{GIM}–TEC

_{CIR}are higher for HSA, the highest precision (related to the standard deviation) and accuracy (related to NRMSE) of TEC

_{GIM}is reached during HSA, for both quiet and disturbed conditions. This feature slightly degrades moving from north to south. For LSA, it can be noted that the accuracy is considerably lower in the southern station RESU.

## 4. Summary and Conclusions

_{p}to assess separately the disturbed periods (K

_{p}≥ 3

^{+}) from the quiet ones (K

_{p}< 3

^{+}). Concerning the disturbed conditions, the period of March 2015, including the severe St. Patrick geomagnetic storm occurrence on 17–19 March 2015, has also been considered. TEC

_{CIR}values obtained through the Ciraolo et al. [17] method have been calibrated using RINEX files recorded every 30 s at STUE, INGR and RESU. After performing the calibration, a 5 min running mean has been applied to smooth out any possible spike characterizing the time series. Finally, to be consistent with the 2 h time resolution of GIMs, for each day of selected periods, values corresponding at 00, 02, …, 20, 22 UT have been considered.

_{GIM}and TEC

_{CIR}values are highly correlated, but TEC

_{GIM}values are always greater than TEC

_{CIR}values, independently of solar and geomagnetic activity, hour of the day, season and latitude. This could be ascribed to the different assumptions made for the DCB estimation by IGS and Ciraolo algorithm. Anyhow, the difference (TEC

_{GIM}–TEC

_{CIR}) significantly increases as the solar activity increases. With regard to this, it has to be considered that during HSA periods there is an increase of the solar extreme ultraviolet radiation, with a consequent intensification of electric fields in the upper atmosphere; this fact, for instance, increases the vertical

**E**×

**B**drift (where

**E**is the equatorial zonal electric field and

**B**the geomagnetic field) at low latitudes, with a consequent enhancement of the growth of instability processes like the Rayleigh-Taylor one, which are at the base of the ionospheric irregularities formation [38,39]. Therefore, the increased difference (TEC

_{GIM}–TEC

_{CIR}) for HSA could mean that GIMs find it more difficult to manage the corresponding growth of ionospheric irregularities.

_{GIM}–TEC

_{CIR}) is higher for geomagnetic disturbed conditions than for geomagnetic quiet ones, especially during the early phase of a geomagnetic storm when very large values are obtained. This difference is also affected by a latitudinal dependence, increasing from the north to the south of Italy. This confirms the results found by previous studies [14,17], which found that GIMs are more reliable at mid-latitudes than at low-latitudes.

_{GIM}–TEC

_{CIR}) differences are higher for HSA, the corresponding relative errors are lower than those characterizing LSA.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

_{p}data. The authors also wish to acknowledge the contributions of all people involved in the managing of ground GPS stations of the Italian “Rete Integrata Nazionale GNSS (RING)” managed by INGV, and they also thank three anonymous reviewers for their valuable comments. Parts of the project were funded by the German DFG project DEAREST (SCHU 1103/15-1).

## Conflicts of Interest

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**Figure 1.**Scatterplots (TEC

_{GIM}vs. TEC

_{CIR}) and corresponding linear regressions for STUE (upper row), INGR (middle row) and RESU (lower row) for the LSA period between July 2008 and June 2009. Left panels refer to quiet geomagnetic values (K

_{p}< 3

^{+}), while right panels refer to disturbed geomagnetic values (K

_{p}≥ 3

^{+}). The number of considered measurements N is shown inside each plot.

**Figure 2.**Scatterplots (TEC

_{GIM}vs. TEC

_{CIR}) and corresponding linear regressions for STUE (upper row), INGR (middle row) and RESU (lower row) for the HSA period between September 2013 and August 2014. Left panels refer to quiet geomagnetic values (K

_{p}< 3

^{+}), while right panels refer to disturbed geomagnetic values (K

_{p}≥ 3

^{+}). The number of considered measurements N is shown inside each plot.

**Figure 3.**Daily variation of the difference (TEC

_{GIM}- TEC

_{CIR}) in terms of hourly mean and corresponding standard deviation, with a time resolution of 2 h (corresponding with the time resolution of GIMs), for STUE (upper row), INGR (middle row) and RESU (lower row). Left panels refer to quiet geomagnetic values (K

_{p}< 3

^{+}), while right panels refer to disturbed geomagnetic values (K

_{p}≥ 3

^{+}). For this analysis the LSA period (July 2008–June 2009) was joined to the HSA period (September 2013–August 2014).

**Figure 4.**Mean monthly variation of the difference (TEC

_{GIM}- TEC

_{CIR}), and corresponding standard deviation, for STUE (upper row), INGR (middle row) and RESU (lower row). Left panels refer to quiet geomagnetic values (K

_{p}< 3

^{+}), while right panels refer to disturbed geomagnetic values (K

_{p}≥ 3

^{+}). For this analysis the LSA period (July 2008–June 2009) was joined to the HSA period (September 2013–August 2014).

**Figure 5.**Daily variation of the difference (TEC

_{GIM}- TEC

_{CIR}) in terms of hourly mean and corresponding standard deviation, with a time resolution of 2 h (corresponding with the time resolution of GIMs), for STUE (upper row), INGR (middle row) and RESU (lower row) for the LSA period between July 2008 and June 2009. Left panels refer to quiet geomagnetic values (K

_{p}< 3

^{+}), while right panels refer to disturbed geomagnetic values (K

_{p}≥ 3

^{+}).

**Figure 6.**Mean monthly variation of the difference (TEC

_{GIM}-TEC

_{CIR}), and corresponding standard deviation, for STUE (upper row), INGR (middle row) and RESU (lower row) for the LSA period between July 2008 and June 2009. Left panels refer to quiet geomagnetic values (K

_{p}< 3

^{+}), while right panels refer to disturbed geomagnetic values (K

_{p}≥ 3

^{+}).

**Figure 7.**Daily variation of the difference (TEC

_{GIM}- TEC

_{CIR}) in terms of hourly mean and corresponding standard deviation, with a time resolution of 2 h (corresponding with the time resolution of GIMs), for STUE (upper row), INGR (middle row) and RESU (lower row) for the HSA period between September 2013 and August 2014. Left panels refer to quiet geomagnetic values (K

_{p}< 3

^{+}), while right panels refer to disturbed geomagnetic values (K

_{p}≥ 3

^{+}).

**Figure 8.**Mean monthly variation of the difference (TEC

_{GIM}- TEC

_{CIR}), and corresponding standard deviation, for STUE (upper row), INGR (middle row) and RESU (lower row) for the HSA period between September 2013 and August 2014. Left panels refer to quiet geomagnetic values (K

_{p}< 3

^{+}), while right panels refer to disturbed geomagnetic values (K

_{p}≥ 3

^{+}).

**Figure 9.**Scatterplots (TEC

_{GIM}vs. TEC

_{CIR}) (left panels) and difference (TEC

_{GIM}–TEC

_{CIR}) (right panels) for the whole month of March 2015, for STUE (upper row), INGR (middle row) and RESU (lower row). The number of considered measurements N is shown inside each of the left plots. K

_{p}values are plotted in red for the whole month in each of the right panels.

**Figure 10.**Taylor diagram summarizing the main statistical parameters of the considered datasets. Black y-axis represents the standard deviation of each TEC

_{GIM}dataset normalized to the corresponding TEC

_{CIR}dataset. Blue x-axis reports the normalized (or centered) root mean square error and the orange circular curve represents the correlation coefficient. Red, blue and green symbols identify the datasets related to INGR, STUE and RESU respectively. Different symbols show different combinations of solar (low and high) and geomagnetic (quiet and disturbed) conditions.

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**MDPI and ACS Style**

Tornatore, V.; Cesaroni, C.; Pezzopane, M.; Alizadeh, M.M.; Schuh, H.
Performance Evaluation of VTEC GIMs for Regional Applications during Different Solar Activity Periods, Using RING TEC Values. *Remote Sens.* **2021**, *13*, 1470.
https://doi.org/10.3390/rs13081470

**AMA Style**

Tornatore V, Cesaroni C, Pezzopane M, Alizadeh MM, Schuh H.
Performance Evaluation of VTEC GIMs for Regional Applications during Different Solar Activity Periods, Using RING TEC Values. *Remote Sensing*. 2021; 13(8):1470.
https://doi.org/10.3390/rs13081470

**Chicago/Turabian Style**

Tornatore, Vincenza, Claudio Cesaroni, Michael Pezzopane, Mohamad Mahdi Alizadeh, and Harald Schuh.
2021. "Performance Evaluation of VTEC GIMs for Regional Applications during Different Solar Activity Periods, Using RING TEC Values" *Remote Sensing* 13, no. 8: 1470.
https://doi.org/10.3390/rs13081470