The Ionospheric Three-Dimensional Electron Density Variations Induced by the 21 August 2017 Total Solar Eclipse by Using Global Ionospheric Specification

Abstract

Global Ionospheric Specification (GIS) is based on the Gauss–Markov Kalman filter to assimilate the slant total electron content (TEC) observed from ground-based GPS receivers and space-based radio occultation instrumentations in order to reconstruct three-dimensional (3D) ionospheric electron density structure, and it can remotely sense and monitor the weather condition in space. In this study, five minutes of high temporal resolution GIS is implemented in order to reconstruct the 3D electron density structure on the 21 August 2017 total solar eclipse and analyze the variations induced by the moon’s shadow. To obtain more information of the ionosphere, from the extend 2200 GPS stations on the continental United States, are added for assimilation. The results show the ionosphere peak height (hmF2) uplift was 30–50 km altitude in latitude 25–40°N, and that the electron density depletion at higher altitudes (400 km) has a more noticeable time delay than at low altitudes (200 km), especially in low-latitude regions.

1. Introduction

The impact of solar eclipses on the ionosphere has been studied for several decades. Initially, scientists used ground radio wave sounding to measure the influence on the ionosphere during the obscuration. Mitra et al. [1] used radio sounding to detect the influence of obscuration on the ion content in the E and F layer, while Evans [2] applied the incoherent backscatter method to study the ionospheric vertical structure during an eclipse. Cheng et al. [3] used multi-ground radio measurements to study the solar eclipse effect on the equatorial ionosphere, and Tsai and Liu [4] used the digisonde to observe solar eclipse-induced atmospheric gravity waves. Liu et al. [5] examined the vertical phase and group propagation of eclipse-triggered gravity waves using digisonde sounding. Ground radio sounding provides ionospheric variations observation in the vertical direction. However, the sounding coverage is limited around the station location, and the ionospheric variations in the horizontal direction cannot be retrieved.

In addition to ground radio sounding, the ground-based station receives dual-frequency GPS signals that can calculate total electron content (TEC) measurements and provide regional ionospheric horizontal information. Liu et al. [6] analyzed the ionospheric variations during a solar eclipse using GPS vertical TEC observations, while Tsai and Liu [7] examined the ionospheric response to the eclipse over a large area using the GPS TEC network. Liu et al. [8] presented the moon’s shadow-induced bow and stern waves by using TEC measurements. Although ground-based GPS observation can obtain continuity regional horizontal information, detecting the complete variation during obscuration is still challenging.

On 21 August 2017, a total solar eclipse passed over the continental United States (CONUS) from the west to the east coast. During the period of interest, more than 2000 ground-based GNSS receivers from the International GNSS (Global Navigation Satellite System) Service (IGS) and Continuously Operating Reference Station (CORS) networks were observing the ionosphere (Figure 1). The massive TEC observations monitored ionospheric variations in the horizontal direction during the eclipse, and numerous dramatic signatures were reported. Coster et al. [9] investigated the presence of enhanced large-scale traveling ionospheric disturbances (TIDs) during the eclipse, while Zhang et al. [10] detected the ionospheric bow waves during obscuration. Sun et al. [11] revealed that the moon shadow-induced acoustic shockwave resulted in the bow wave trough and crest near the totality path. In addition to horizontal observations, there were also reports of vertical soundings during the solar eclipse. Reinisch et al. [12] used digisonde observation to detect the rapid vanishing of f_oE and f_oF1 during the obscuration at the Idaho National Laboratory, while Bullett and Mabie [13] used ionosonde to vertically and obliquely sound the ionosphere affected by the totality. In addition to the vanishing of the electron density, Tain et al. [14] detected the enhancement of the electron density near the first contact of the total solar eclipse by using TEC and ionosonde observation.

Various ionospheric modeling and reconstructions were also employed. Huba and Drob [15] applied the SAMI3 model to simulate the influence on the ionosphere, while Wang et al. [16] implemented the high-resolution thermosphere-ionosphere-electrodynamics general circulation model (TIE-GCM) to investigate the response of F2 region electron density (Ne) at Millstone Hill to the Solar Eclipse. The Global Ionosphere-Thermosphere Model (GITM) was used to simulate the influence of the total solar eclipse of 21 August 2017 and compared with the ground-based GNSS TEC and ionosondes measurements [17]. He et al. [18] and Chen et al. [19] applied the tomography method to reconstruct the three-dimensional (3D) electron density distribution by using ground-based GNSS TEC to analyze the variation induced by the eclipse. Moreover, Chen et al. [20] assimilated vertical TEC into TIE-GCM to reanalyze the ionosphere influenced by the eclipse.

The Global Ionospheric Specification (GIS) is an ionospheric data assimilation model based on the Gauss-Markov Kalman filter [21,22]. It assimilates slant TEC observation from ground-based GPS receiving stations [23,24] and space-based radio occultation (RO) instrumentations, such as FORMOSAT-3/COSMIC (F3/C), into a background model [25,26,27] to provide a continuity 3D electron density distribution of the ionosphere. Lin et al. [25] used an empirical orthogonal function to generate a location-dependent non-stationary background model error covariance together with a Kalman filter measurement update step to build a preliminary ionospheric data assimilation model. To increase the accuracy of the analysis of electron density structure, Lin et al. [26] applied a recursive forecast and measurement update steps in a Kalman filter. In addition, Lin et al. [27] assimilated FORMOSAT-7/COSMIC-2 (F7/C2) RO slant TEC into GIS and validated the results with digisonde stations in low- and mid-latitude, demonstrating GIS’s ability to reconstruct the ionospheric structures.

The objective of the study is to use GIS for reconstructing the 3D electron density distribution during the total solar eclipse on 21 August 2017 and to detect the 3D variation induced by the obscuration. To achieve this goal, a high temporal resolution (5 min) GIS is implemented, and an additional 2200 of ground-based GNSS receiving station data located in North America are assimilated into the GIS to reconstruct the variation of the electron density.

2. Global Ionospheric Specification

GIS was utilized to reconstruct the 3D ionospheric electron density during the total solar eclipse, with the approach based on the work of Lin et al. [25,26]. Figure 2 illustrates the flowchart of GIS. The data assimilation approach used in GIS is the Gauss–Markov Kalman filter, which consists of a forecast step and a measurement update step. In each time step, GIS first applies the forecast step to predict the current state vector (electron density) and model error covariance, and it then assimilates observation data in the measurement update step. The equations for the measurement update step include the state vector update, model error covariance update, and the Kalman gain, as shown below:

(1)${\mathbf{x}}_k^{\mathrm{a}}={\mathbf{x}}_k^{\mathrm{f}}+{\mathbf{K}}_k{(\mathbf{y}}_k-{\mathbf{H}}_k{\mathbf{x}}_k^{\mathrm{f}})$

(2)${\mathbf{P}}_k^{\mathrm{a}}=(\mathbf{I}-{\mathbf{K}}_k{\mathbf{H}}_k){\mathbf{P}}_k^{\mathrm{f}}$

(3)${\mathbf{K}}_k=\frac{{\mathbf{P}}_k^{\mathrm{f}}{\mathbf{H}}_k^T}{{\mathbf{H}}_k{\mathbf{P}}_k^{\mathrm{f}}{\mathbf{H}}_k^T+{\mathbf{R}}_k}$

where x^a is the analysis state vector, x^f is forecast state vector, K is the Kalman gain, y is the observation data, H is the matrix related to the observation geometry, P^a is the analysis model error covariance, P^f is the forecast model error covariance, I is the diagonal matrix, R is the data error covariance, and k is the kth time step. Equation (1) represents the measurement update of the state vector, where the observation data (slant TEC) is assimilated into the state vector. The background model used by GIS is the ionospheric empirical model International Reference Ionosphere, and the version used is IRI-2016 [28]. Equation (2) represents the measurement update of the model error covariance. The model error covariance needs to be updated as the state vector is updated by the observation. Equation (3) represents the Kalman gain, which uses the model error covariance and the observational data error covariance to determine the influence of observation on the state vector and the model error covariance.

On the other hand, the equations for the forecast step include the state vector forecast (Equation (4)) and the model error covariance forecast (Equation (5)), as shown below:

(4)${\mathbf{x}}_{k+1}^{\mathrm{f}}=B\mathbf{M}{\mathbf{x}}_k^{\mathrm{a}}+(1-B){\mathbf{x}}_{k+1}^{\mathrm{b}}$

(5)${\mathbf{P}}_{k+1}^{\mathrm{f}}=B^2\mathbf{M}{\mathbf{P}}_k^{\mathrm{a}}{\mathbf{M}}^T+{(1-B)}^2{\mathbf{P}}_{k+1}^{\mathrm{b}}+\mathbf{Q}$

where x^b is background state vector, B is the ratio of merging the forecast state vector and the background state vector, M is the west shifting matrix, P^b is the background model error covariance, Q is process noise covariance, and k + 1 is the k + 1th time step. Since IRI is an ionospheric empirical model, it cannot forecast the state vector of the next time step based on the previous state vector. To represent the background model prediction, GIS shifts the previous time step analysis electron density by 15 degrees per hour in the geomagnetic coordinate. The forecast step of the state vector is then created by merging part of the west-shifting state vector and part of the background state vector. In the standard temporal resolution, the merging ratio B is set to 0.9, meaning that 90% of the shifting state vector and 10% of the background state vector are merged. The flowchart of GIS shows that the background state vector of IRI-2016 and its corresponding model error covariance are the input of the forecast step, while the observation data and the corresponding data error covariance are the input of the measurement update step. The output of GIS is the analysis electron density at each time step.

The spatial resolutions of GIS for the longitude, latitude, and altitude are 5 degrees, 2.5 degrees, and 20 km, respectively. However, an hourly temporal resolution is inadequate for studying the ionospheric variations induced by obscuration as the moon’s shadow moves quickly. To investigate the impact of the eclipse, we increased the temporal resolution from 1 h to 5 min. For high temporal resolution, the merging ratio B is set to 0.99 to ensure a sufficient proportion of the west-shifting state vector within the forecast state vector. When increasing the temporal resolution, it is also necessary to increase the amount of observational data. While standard GIS assimilates approximately 1000 worldwide ground-based GPS observations and F3/C (F7/C2) RO observations, this may be insufficient for a 5-min resolution. Additionally, F3/C has only one microsatellite in operation, which was not located over North America during the obscuration, creating a data gap. To address this, the GIS assimilates an additional 2200 of ground-based GNSS receiving station data located in North America. All the ground-based GNSS receiving stations used for GIS assimilation are shown in Figure 1, and the dense ground-based slant TEC data provide high spatial and temporal resolution information to reconstruct the horizontal and vertical electron density structure of the ionosphere.

3. Results

Here, we implement the 3D electron density produced by the GIS to reconstruct the ionospheric variation induced by the solar eclipse. Given that the moon’s shadow travels rapidly across the earth, the standard temporal resolution of GIS (1 h) is not suitable, and we implement a high temporal resolution (5 min) to assimilate both the standard dataset (about 1000 ground-based GNSS stations and F3/C) and the extra dataset (about 2200 ground-based GNSS stations) on 19 August 2017 and finish on 21 August 2017. It is noteworthy that only the GIS on 20 August and 21 August is used, since Lin et al. [26] reveal that the GIS needs about 8 to 10 h to reduce the model error. The GIS electron density distributions on 20 August 2017 are set as the normal day to compare the influence induced by the eclipse. Figure 3 illustrates the horizontal electron density distributions at 200, 300, and 400 km altitudes at 18:30 UTC during obscuration. The electron density depleted at 200 km altitude around the maximum obscuration of around 90°W. However, the electron density depletion at 300 and 400 km altitude is located around 100°W and 110°W at 300 and 400 km altitudes, respectively.

The peak electron density (NmF2) and peak height (hmF2) at the F2 layer are used to represent the vertical status of the ionosphere. The GIS time-latitudinal distributions of hmF2 and NmF2 at longitudes of 120°W, 110°W, 100°W, 90°W, and 80°W on the eclipse day and the normal day are shown in Figure 4. On the normal day, the GIS shows that NmF2 is generally higher in the low latitude region and lower in the mid- and high-latitude region. However, on the eclipse day, the GIS NmF2 is significantly depleted within latitude 25–45°N due to the moon’s shadow. Comparing the NmF2 distributions for the eclipse day and the normal day, the GIS NmF2 at all different longitudes is significantly depleted during the obscuration. The GIS hmF2 time-latitude distributions on 20 August 2017 show that the ionospheric peak height declines smoothly from low latitude to high latitude, with uplift due to the fountain effect of an equatorial ionized anomaly between UTC 17:00 and 19:55. On the eclipse day, the hmF2 distributions are extremely different from the normal day. The GIS shows that the hmF2 uplift dramatically between latitudes of 25 and 40°N.

In addition to hmF2 and NmF2, the altitudinal electron density profile spanning from the bottom side to the top side of the ionosphere provides more detailed information in the vertical direction. Figure 5 and Figure 6 illustrate the time-altitude distribution of the GIS electron density between longitudes of 120°W to 80°W and latitudes of 25°N to 55°N for both the normal day and the eclipse day. Note that the solid black lines in Figure 6 indicate the obscuration percentage. The time and altitude distributions of the GIS electron density on the normal day represent the vertical state of the non-eclipse ionosphere. In contrast, the electron density distributions on the eclipse day have drastic variations, as shown in Figure 6. The electron density is significantly depleted during and after obscuration at each location affected by the eclipse. To understand the influence of the moon’s shadow on the ionosphere, we subtract the normal day electron density from the eclipse day electron density to calculate the discrepancy from the obscuration, as shown in Figure 7. The percentage of discrepancy reveals that the impact of the eclipse is dissimilar at different locations, possibly due to the latitude, local time, and obscuration distribution. Furthermore, the discrepancy also shows that the electron density depletion at different altitudes is not the same, with the electron density depletion and recovery occurring earlier at low altitudes and late at peak altitudes.

4. Discussion

The ionosphere’s electron density depletion during the eclipse and subsequent uplift was also observed in other studies, including [2,3,5,29]. The interruption of the photoionization process by the moon’s shadow during the obscuration is believed to be the main cause of this phenomenon. Table 1 denotes the average hmF2 difference between the eclipse day and the normal day from UTC 17:00 to 19:55 in 25–40°N and 42.5–55°N. The hmF2 on an eclipse day commonly uplifts 30–50 km altitude in the latitudes of 25–40°N, while it declines 10 to 20 km in 42.5–55°N. The rapid vanishing of electron density in the E-layer during the obscuration, caused by the attenuation of the ionospheric E-layer photochemical process, resulted in the uplift of hmF2. The hmF2 distribution from the low to mid-latitude region is also significantly different between a normal day and eclipse day (Figure 4). On normal days, hmF2 smooth decreases from the low-latitude to the mid-latitude region, while during the obscuration period, it steeply decreases around 40°N. Figure 8 further illustrates the time-latitude distribution of hmF2 gradient at 120°W, 110°W, 100°W, 90°W, and 80°W on eclipse and normal days. Comparing the hmF2 gradient distributions, the hmF2 gradient decreases significantly around the 25–40°N latitude during and after the obscuration. From the gradient distribution of hmF2, it can be observed that the maximum gradients are located around latitude 40 degrees and occur only after peak obscuration. This also explains the attenuation of the ionospheric E-layer photochemical process caused by the moon’s shadows that takes time to impact the electron density of the F-layer.

On the other hand, the discrepancies in time-altitude distributions also suggest that electron density depletions have altitudinal time delay at different latitudes, which is especially significant in low latitudes (Figure 7). For instance, the discrepancy at longitude 90°W and latitude 30°N shows that the electron density at 200 km altitude starts depleting around UTC 17:30 and recovers around UTC 20:00. However, the electron density at 400 km altitude starts depleting around UTC 19:00 and recovers around UTC 21:00. Furthermore, horizontal electron density distributions at different altitudes also demonstrate electron density depletions having an altitudinal time delay in Figure 3. The totality at UTC 18:30 arrived around 90°W, and the electron density depleted at 200 km altitude around the maximum obscuration. Nevertheless, the maximum depletions of electron density at 300 and 400 km altitudes were around 100°W and 110°W on the totality path. This result demonstrates that the time delay of electron density depletion is longer at higher altitudes.

Wang et al. [16] observed and simulated a time delay between the most significant depletion of electron density in the F2 layer and the occurrence of the local maximum obscuration. Further, the delay time increases with altitude. Figure 9 illustrates the distributions of the delay time between the maximum electron density depletion and the peak obscuration. The delay time is evidently longer at peak altitude than at low altitude, especially in the low-latitude region. Table 2 reveals the average delay time between maximum electron density depletion and maximum obscuration. In latitude 25–40°N, the average delay time is 45 min at altitudes of 120–300 km and 77 min at altitudes of 320–500 km. In latitude 45–55°N, the average delay time is 30 min at altitudes of 120–300 km and 34 min at altitudes of 320–500 km. The discrepancies in the GIS electron density suggest that the delay time between maximum electron density depletion and maximum obscuration is shorter at low altitudes and longer at peak altitudes, which is in agreement with Wang et al. [16]. Moreover, Liu et al. [30] suggest that the plasma transport of E×B drifts (equatorial fountain effect) and lunar gravitation forces could lead to the longer delay time in low latitudes.

Furthermore, Tain et al. [14] observed an increase in ionosonde NmF2 near the first contact, particularly in the northern and central areas of CONUS, specifically at Idaho National LAB (43.81°N, 112.68°W) and Boulder (40°N, 105.3°W). The discrepancies in GIS electron density (Figure 7) also reveal enhancements in the F2 layer near the ionosonde areas at UTC 16:00 during the first contact, consistent with the NmF2 variability detected by Tain et al. [14]. The reconstruction of enhancements demonstrates that the GIS not only reproduces the depletion of electron density influenced by the moon’s shadow but also captures the increase in electron density during the first contact.

GIS assimilates ground-based GNSS and space-based RO observations to produce 3D electron density with both horizontal and vertical information. However, during the obscuration, the only operating microsatellite of F3/C was not positioned over North America, resulting in the absence of space-based RO sounding to provide vertical information of the ionosphere. Fortunately, the totality path of the solar eclipse passed through the region with highest concentration of ground-based GNSS receiving stations. The slant TEC data from these stations not only provided horizontal information but also partial vertical information of the ionosphere. By assimilating observations from 2200 stations in North America, a significant amount of vertical information was accumulated, allowing for the successful reconstruction of the 3D electron density structure. This solar eclipse event provided a unique opportunity to study 3D variations of the ionosphere due to the abundance of observational data. Insufficient observational data may hinder the accurate reconstruction of 3D ionospheric variations.

5. Conclusions

This study employs the data assimilation model GIS to reconstruct the ionosphere during the total solar eclipse on 21 August 2017. The GIS assimilates approximately 3000 ground-based GNSS receiving slant TEC and increases the temporal resolution to produce a 5-min temporal resolution 3D electron density structure. The analysis results of the GIS show significant depletion of electron density from the E-layer to F-layer, simultaneously leading to an uplift of the ionosphere. The dense ground-based GNSS slant TEC provides both enough horizontal and vertical ionospheric information during obscuration and allows the GIS to detect the 3D variations, even though the F3/C RO observation did not sound the continent of North America. We draw three conclusions. The first conclusion is that the ionospheric peak height uplifts significantly during obscuration compared to the normal day, generally uplifting 30–50 km altitude in latitude 25–40°N. The second conclusion is that electron density depletion at higher altitudes (320–500 km) has a more noticeable delay time than at low altitudes (120–300 km), especially in low-latitude regions. The third conclusion is that with enough observations for assimilating, the GIS has the capability to reconstruct high temporal resolution ionospheric 3D variations induced by the solar eclipse.

Author Contributions

Conceptualization, C.-Y.L. and J.-Y.L.; methodology, C.-Y.L.; software, C.-Y.L.; validation, C.-Y.L., J.-Y.L., C.C.-H.L. and M.-Y.C.; formal analysis, C.-Y.L.; investigation, C.-Y.L., J.-Y.L., C.C.-H.L. and M.-Y.C.; resources, C.-Y.L.; data curation, C.-Y.L.; writing—original draft preparation, C.-Y.L.; writing—review and editing, J.-Y.L., C.C.-H.L. and M.-Y.C.; visualization, C.-Y.L.; supervision, C.-Y.L.; project administration, C.-Y.L., J.-Y.L. and C.C.-H.L.; funding acquisition, C.-Y.L., J.-Y.L. and C.C.-H.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

FORMOSAT-3/COSMIC data were obtained online (https://data.cosmic.ucar.edu/gnss-ro/cosmic1/postProc/, https://tacc.cwb.gov.tw/data-service/fs3_cosmic/, accessed on 23 August 2017). The source code of IRI-2016 is taken online (http://irimodel.org/IRI-2016/, accessed on 5 September 2017). The RINEX files of the ground-based GPS data were obtained online (http://garner.ucsd.edu/, https://geodesy.noaa.gov/corsdata/, accessed on 23 August 2017).

Acknowledgments

The authors gratefully acknowledge the COSMIC Data Analysis and Archive Center (CDAAC) and Taiwan Analysis Center for COSMIC (TACC) for providing FORMOSAT-3/COSMIC data, the International Reference Ionosphere (IRI) working group for providing the Fortran source code of IRI-2016, and the International GNSS Service (IGS) and Continuously Operating Reference Station (CORS) for providing the ground-based GPS data.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Tables

Figure 1. The totality trace of 21 August 2017 from west to east in the continent of North America. The red dots denote the time and location of totality at longitudes of 120°W, 110°W, 100°W, 90°W, and 80°W. The blue triangles indicate the locations of used ground-based GNSS receivers.

Figure 2. The flowchart of Global Ionospheric Specification.

Figure 3. The electron density horizontal distributions over North America at 200, 300, and 400 km altitudes produced by the GIS at UTC 18:30 on 21 August 2017.

Figure 4. The time and latitude distributions of GIS peak density and peak height at the solar eclipse day (DOY 233, 21 August 2017) and the normal day (DOY 232, 20 August 2017) at longitude 120°W, 110°W, 100°W, 90°W, and 80°W. The color contours represent the peak density distributions and the structures denote the peak height distributions.

Figure 5. The time and altitude distributions of GIS electron density at the normal day (DOY 232, 20 August 2017) at longitude 120°W, 110°W, 100°W, 90°W, and 80°W as well as at latitude 25°N, 30°N, 35°N, 40°N, 45°N, and 50°N.

Figure 6. The time and altitude distributions of GIS electron density at solar eclipse day (DOY 233, 21 August 2017) at longitude 120°W, 110°W, 100°W, 90°W, and 80°W as well as at latitude 25°N, 30°N, 35°N, 40°N, 45°N, and 50°N. The black solid lines represent the obscuration.

Figure 7. The time and altitude distributions of the GIS electron density difference between solar eclipse day (DOY 233, 21 August 2017) and the normal day (DOY 232, 20 August 2017) at longitude 120°W, 110°W, 100°W, 90°W, and 80°W as well as at latitude 25°N, 30°N, 35°N, 40°N, 45°N, and 50°N. The black solid lines represent the obscuration.

Figure 8. The time-latitude distributions of the hmF2 gradient at solar eclipse day (DOY 233, 21 August 2017) and the normal day (DOY 232, 20 August 2017) at longitude 120°W, 110°W, 100°W, 90°W, and 80°W. The contours represent the percentage of obscuration.

Figure 9. The median value of time difference between the maximum electron density depletion and maximum obscuration at 120–200 km, 220–300 km, 320–400 km, and 420–500 km altitude.

Table 1

The average hmF2 difference between eclipse day and normal day from UTC 1700 to 1955.

	120°W	110°W	100°W	90°W	80°W
25–40°N	49.2 km	51.9 km	44.6 km	45.9 km	31.1 km
42.5–55°N	−11.6 km	−18.3 km	−15.7 km	−18.9 km	−6.6 km

Table 2

The average delay time between maximum electron density depletion and maximum obscuration.

	120–300 km	320–500 km
25, 30, 35, 40°N120, 110, 100, 90, 80°W	45 min	77 min
45, 50, 55°N120, 110, 100, 90, 80°W	30 min	34 min

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