Figure 1.
Causes of abnormal correction in a voxel. (a) Sketch of voxels, a bubble and rays in a tomographic model. Usually, the whole STEC of the ray AC is adopted in tomographic inversion due to the difficulty in removing the contribution of the plasmasphere (i.e., the part of CE). However, only part of the EF should be responsible for the tomographic inversion. (b) Sketch of abnormal correction in a particular ray. Suppose that the solid profile shown on the right is the current state of ray AD shown on the left, and there is an abnormal correction on voxel III brought by ray BC. The abnormal correction will certainly lead to the model STEC along ray AD being unusually larger or smaller, which, in turn, may result in an abnormal correction for other associated voxels, e.g., voxel II.
Figure 1.
Causes of abnormal correction in a voxel. (a) Sketch of voxels, a bubble and rays in a tomographic model. Usually, the whole STEC of the ray AC is adopted in tomographic inversion due to the difficulty in removing the contribution of the plasmasphere (i.e., the part of CE). However, only part of the EF should be responsible for the tomographic inversion. (b) Sketch of abnormal correction in a particular ray. Suppose that the solid profile shown on the right is the current state of ray AD shown on the left, and there is an abnormal correction on voxel III brought by ray BC. The abnormal correction will certainly lead to the model STEC along ray AD being unusually larger or smaller, which, in turn, may result in an abnormal correction for other associated voxels, e.g., voxel II.
Figure 2.
Distribution of GNSS stations, ionosonde stations and the trajectories of Swarm satellites over the study period. Black dots and blue crosses are the GNSS stations for inversions and validations, respectively. Red stars are ionosonde stations. Blue, red and green lines are the trajectories of Swarm satellites.
Figure 2.
Distribution of GNSS stations, ionosonde stations and the trajectories of Swarm satellites over the study period. Black dots and blue crosses are the GNSS stations for inversions and validations, respectively. Red stars are ionosonde stations. Blue, red and green lines are the trajectories of Swarm satellites.
Figure 3.
Voxels covered by GNSS rays. (a) The number of voxels that are traversed by GNSS rays in each vertical column (i.e., pixel) at 00:00 universal time (UT) on 15 March 2015 with white color indicating that none of the voxels were crossed in that column. (b) The average number of associated rays for the voxels in a vertical column during the whole study period. The value of each pixel is computed by the sum of the associated ray number in each column divided by the number of voxels in each column (i.e., 55 here), and then averaged over the whole period. (c) The average number of associated rays at different heights for the voxels during the whole study period.
Figure 3.
Voxels covered by GNSS rays. (a) The number of voxels that are traversed by GNSS rays in each vertical column (i.e., pixel) at 00:00 universal time (UT) on 15 March 2015 with white color indicating that none of the voxels were crossed in that column. (b) The average number of associated rays for the voxels in a vertical column during the whole study period. The value of each pixel is computed by the sum of the associated ray number in each column divided by the number of voxels in each column (i.e., 55 here), and then averaged over the whole period. (c) The average number of associated rays at different heights for the voxels during the whole study period.
Figure 4.
Kp and Dst indices with UT hour on 15–20 March 2015.
Figure 4.
Kp and Dst indices with UT hour on 15–20 March 2015.
Figure 5.
Temporal variations in vertical density at ionosonde station (a) DB049, (b) JR055 and (c) PQ052 over the study period. The four rows (from top to bottom) in each subplot correspond to the results of ionosonde, RACR algorithm, MART algorithm and IRI2016 model, respectively. Pixels with no data are filled with white color.
Figure 5.
Temporal variations in vertical density at ionosonde station (a) DB049, (b) JR055 and (c) PQ052 over the study period. The four rows (from top to bottom) in each subplot correspond to the results of ionosonde, RACR algorithm, MART algorithm and IRI2016 model, respectively. Pixels with no data are filled with white color.
Figure 6.
Comparisons of electron density profile at station DB049 at four-hour intervals on 15 March 2015 starting at UT 00:00.
Figure 6.
Comparisons of electron density profile at station DB049 at four-hour intervals on 15 March 2015 starting at UT 00:00.
Figure 7.
Comparisons of electron density profile at station DB049 at four-hour intervals on 17 March 2015.
Figure 7.
Comparisons of electron density profile at station DB049 at four-hour intervals on 17 March 2015.
Figure 8.
The error (unit: 1011/m3) and the RMS (unit: 1011/m3) of the derived NmF2 at ionosonde stations (a) DB049, (b) JR055 and (c) PQ052 with the ionosonde observations as the ground-truth. “M” and “R” in the bracket refer to the MART algorithm and RACR algorithm, respectively. Each point of the data for the error corresponds to an error in each epoch, and each column of the data for the RMS corresponds to the statistic of the whole day. Notice that the scales of the error and the RMS for (c) are several times that of the other two.
Figure 8.
The error (unit: 1011/m3) and the RMS (unit: 1011/m3) of the derived NmF2 at ionosonde stations (a) DB049, (b) JR055 and (c) PQ052 with the ionosonde observations as the ground-truth. “M” and “R” in the bracket refer to the MART algorithm and RACR algorithm, respectively. Each point of the data for the error corresponds to an error in each epoch, and each column of the data for the RMS corresponds to the statistic of the whole day. Notice that the scales of the error and the RMS for (c) are several times that of the other two.
Figure 9.
The error (unit: km) and the RMS (unit: km) of the derived hmF2 at ionosonde stations (a) DB049, (b) JR055 and (c) PQ052. “M” and “R” in the brackets refer to the MART algorithm and RACR algorithm, respectively. Each point of the data for the error corresponds to an error at each epoch, and each column of the data for the RMS corresponds to the statistic of the whole day. Notice that the scale of RMS for (c) is four times that of the other two.
Figure 9.
The error (unit: km) and the RMS (unit: km) of the derived hmF2 at ionosonde stations (a) DB049, (b) JR055 and (c) PQ052. “M” and “R” in the brackets refer to the MART algorithm and RACR algorithm, respectively. Each point of the data for the error corresponds to an error at each epoch, and each column of the data for the RMS corresponds to the statistic of the whole day. Notice that the scale of RMS for (c) is four times that of the other two.
Figure 10.
The individual RMS (unit: 1010/m3) and its corresponding RMS (unit: 1010/m3) of the reconstructed electron density with the Swarm measurements as the truth-value. “M”, “R”, “A”, “B” and “C” in the brackets refer to the MART algorithm, RACR algorithm, Swarm A, Swarm B and Swarm C, respectively. Each point of the data for the RMS corresponds to the statistic of a continuous profile, and each column of the data for the RMS corresponds to the statistic of the whole day.
Figure 10.
The individual RMS (unit: 1010/m3) and its corresponding RMS (unit: 1010/m3) of the reconstructed electron density with the Swarm measurements as the truth-value. “M”, “R”, “A”, “B” and “C” in the brackets refer to the MART algorithm, RACR algorithm, Swarm A, Swarm B and Swarm C, respectively. Each point of the data for the RMS corresponds to the statistic of a continuous profile, and each column of the data for the RMS corresponds to the statistic of the whole day.
Figure 11.
The individual RMS (unit: TECU) and its corresponding (unit: TECU) of the derived STEC with the GNSS observation as the ground-truth. “M” and “R” in the brackets refer to the MART and RACR algorithms, respectively. Each point of data corresponds to an epoch.
Figure 11.
The individual RMS (unit: TECU) and its corresponding (unit: TECU) of the derived STEC with the GNSS observation as the ground-truth. “M” and “R” in the brackets refer to the MART and RACR algorithms, respectively. Each point of data corresponds to an epoch.
Figure 12.
VTEC maps produced by IGS (left panels), MART (middle panels) and RACR (right panels) at UT 12:00 March 15, 2015 (top panels) and at UT 12:00 March 117 (bottom panels).
Figure 12.
VTEC maps produced by IGS (left panels), MART (middle panels) and RACR (right panels) at UT 12:00 March 15, 2015 (top panels) and at UT 12:00 March 117 (bottom panels).
Figure 13.
Comparisons of electron density profile at station DB049 on 15 March 2015 for the result after STEC correction against those without STEC correction. The curve with a suffix of “_c” corresponds to the result with STEC correction, and vice versa. The epochs for the left and right panels are UT 01:00 and UT 12:00, respectively.
Figure 13.
Comparisons of electron density profile at station DB049 on 15 March 2015 for the result after STEC correction against those without STEC correction. The curve with a suffix of “_c” corresponds to the result with STEC correction, and vice versa. The epochs for the left and right panels are UT 01:00 and UT 12:00, respectively.
Figure 14.
Comparisons of vertical profiles with different and . (a) March 16, 2015 at station PQ052, (b) 17 March 2015 at station PQ052, (c) 15 March 2015 at station PQ052, (d) 18 March at station JR055. σ in the figures stands for the standard derivation. Notice that the solid red and solid blue are almost overlapped in (a,b), solid red, solid blue and red dash are overlapped in (c) and solid blue, blue dash and red dash are almost overlapped in (d).
Figure 14.
Comparisons of vertical profiles with different and . (a) March 16, 2015 at station PQ052, (b) 17 March 2015 at station PQ052, (c) 15 March 2015 at station PQ052, (d) 18 March at station JR055. σ in the figures stands for the standard derivation. Notice that the solid red and solid blue are almost overlapped in (a,b), solid red, solid blue and red dash are overlapped in (c) and solid blue, blue dash and red dash are almost overlapped in (d).
Figure 15.
Percentage of rays that were rejected by the RACR algorithm at each epoch. σ in the figures stands for the standard derivation.
Figure 15.
Percentage of rays that were rejected by the RACR algorithm at each epoch. σ in the figures stands for the standard derivation.
Figure 16.
Comparisons of vertical profiles produced by the MART algorithm employing only rays where outliers had been removed based on the RACR algorithm and all available rays at σ, . Both figures were generated by the MART algorithm on 18 March 2015. The left panel is for DB049, and the right panel is for PQ052.
Figure 16.
Comparisons of vertical profiles produced by the MART algorithm employing only rays where outliers had been removed based on the RACR algorithm and all available rays at σ, . Both figures were generated by the MART algorithm on 18 March 2015. The left panel is for DB049, and the right panel is for PQ052.
Table 1.
The 4-Letter code of GNSS stations selected for independent STEC validation.
Table 1.
The 4-Letter code of GNSS stations selected for independent STEC validation.
AQUI | FATA | JOZ2 | POUS | ZYWI |
---|
AUT1 | GELL | MARS | PRAT | |
BCLN | HOE2 | MDOR | SPT0 | |
BZRG | HOER | MLVL | TARS | |
DENT | IRBE | OSJE | WARE | |
Table 2.
Several parameters used in the tomographic inversions.
Table 2.
Several parameters used in the tomographic inversions.
| Times of Iteration | Temporal Resolution | Elevation Cut-Off |
---|
0.05 | 500 | 15 min | 25o |
Table 3.
The overall RMS of the estimated NmF2 (unit: 1011/m3) and hmF2 (km) for both algorithms and the IRI2016 model over the study period.
Table 3.
The overall RMS of the estimated NmF2 (unit: 1011/m3) and hmF2 (km) for both algorithms and the IRI2016 model over the study period.
Algorithm | Ionosonde | RMS (NmF2) | RMS (hmF2) |
---|
RACR | DB049 | 1.59 | 36.22 |
JR055 | 1.46 | 37.89 |
PQ052 | 1.62 | 28.92 |
MART | DB049 | 1.80 | 43.32 |
JR055 | 1.78 | 49.79 |
PQ052 | 7.50 | 94.44 |
IRI2016 | DB049 | 1.96 | 36.04 |
JR055 | 1.90 | 32.42 |
PQ052 | 1.94 | 27.76 |
Table 4.
The overall RMS of the reconstructed electron density (unit: 1010/m3) by the RACR algorithm, MART algorithm and IRI2016 model over the study period.
Table 4.
The overall RMS of the reconstructed electron density (unit: 1010/m3) by the RACR algorithm, MART algorithm and IRI2016 model over the study period.
Algorithm | Swarm A | Swarm B | Swarm C |
---|
RACR | 9.39 | 6.79 | 9.18 |
MART | 9.69 | 7.47 | 9.80 |
IRI2016 | 10.11 | 7.79 | 9.76 |
Table 5.
The overall RMS (unit: TECU) of the derived VTEC by the RACR algorithm, MART algorithm and IRI2016 model over the whole study period.
Table 5.
The overall RMS (unit: TECU) of the derived VTEC by the RACR algorithm, MART algorithm and IRI2016 model over the whole study period.
| RACR | MART | IRI2016 |
---|
RMS | 2.75 | 3.53 | 9.26 |
Table 6.
The overall RMS (unit: TECU) of the derived VTEC by the RACR algorithm, MART algorithm and IRI2016 model over the whole study period.
Table 6.
The overall RMS (unit: TECU) of the derived VTEC by the RACR algorithm, MART algorithm and IRI2016 model over the whole study period.
| RACR | MART | IRI-2016 |
---|
RMS | 4.99 | 5.31 | 7.51 |