As shown in Figs. 6, 7, and 8, the overall trend of the TC-driven PD events recorded at these weather stations matched except for those observed in the period between September 1–4, 2016 (T-1612 PD), and between August 4–7, 2019 (T-1908 PD). The common feature of these discrepancies can be summarized as follows: The PD negative spikes associated with T-1612 and T-1908 can be seen in the Kagoshima and Yakushima pressure data, but these cannot be seen in Naze data, and vice versa. Since the distance between Kagoshima and Yakushima is 130 km, and the distance between Kagoshima and Naze is 360 km, we expected meso-beta scale pressure anomalies during the aforementioned periods. We also anticipated that these anomalies could be captured with KM.
Figure 9 compares the high elevation angle (HEA) (0.4 < tan θ < 0.8; 25 km < MPL < 50 km at an altitude of 20 km ) (Fig. 9A) and low elevation angle (LEA) (0 < tan θ < 0.4; 50 km < MPL < 506 km at an altitude of 20 km) (Fig. 9B) components of the time-sequential muographic data for the 9 days during which T-1610 and T-1612 caused the local PD. The HEA component represents the muons that passed through a more local atmosphere, closer to KM, and the LEA component represents those muons that passed through a less local atmosphere, further from KM. In Fig. 9C, the time-dependent barometric variations observed at Yakushima and Naze stations31 are presented for reference. As can be seen in Figs. 9A and 9B, there are two muon count rate (MCR) increase events between August 27-September 1 and September 1–5. These MCR increase events were interpreted as PD events associated with T-1610 and T-1612. These events were labeled MCR1610 and MCR1612 here. In Figs. 9A and 9B, we find that the magnitude of HEA-MCR1610 is larger than LEA-MCR1610. Also, we find that the timing and duration are both different between HEA-MCR1612 and LEA-MCR1612. These results are consistent with the pressure variations observed at Yakushima (closer to KM) and Naze (further from KM) stations: PD smaller than that at Yakushima was observed at Naze for T-1610, and at Naze, T-1612 associated PD appeared earlier and lasted longer than Yakushima.
Figure 10. Time-sequential muographic images (A). The four images show the muon flux variations observed every 8 hours within the period between 00:00 on September 3, 2016, and 08:00 on September 4, 2016. The horizontal width of these muographic images corresponds to the shaded area indicated on the map on the right side. The meteorological history of T-1612 is also shown. Triangular symbols indicate the atmospheric pressure gauge stations (Yakushima Station is in the north, and Naze Station is in the south). The symbol KM indicates the location of Kagoshima Muograph. The red numbers and red hollow circles respectively indicate the date and the position of the T-1612's center. The filled red circles indicate the T-1612 positions at 08:00, 16:00 on September 3, and 08:00 on September 4. The red dashed circles indicate the storm area (wind speed > 25 ms− 1) at 00:00, 08:00, 16:00, and 24:00 on September 3, and the brown dashed circles indicate the strong wind area (wind speed > 15 ms− 1) at 00:00 and 24:00 on September 3. The time-dependent variations of the minimum pressure of T-1612 are also shown (B).
Figure 10 shows the time-sequential muographic images taken in the period between 00:00 on September 3, 2016, and 08:00 on September 4, 2016, to analyze the pressure variations caused by the passage of T-1612. In order to cancel the KM's geometrical acceptance and the muon's zenith angular dependence, the number of muon tracks in each pixel was divided by that averaged over a period of 6 months (including the period during the passage of T-1612). Moreover, each pixel was mapped within an elevation angular range between tangents 0.067 and 0.4, and an azimuthal angular range between tangents ± 0.17. This elevation angular range is respectively equivalent to the horizontal range between 300 km and 50 km at an altitude of 20 km. The overall feature is that the large-flux region indicated in the reddish pixels in Fig. 10 was shifted westwards within this period. This large flux-region was interpreted as the low barometric pressure (BP) region associated with the T-1612 passage, and these time-dependent BP variations are consistent with the trajectory of T-1612.
Figure 11 shows the schematic interpretation of the time-sequential muographic images shown in Fig. 10. The distance between KM and the center of T-1612 changed from 180 km to 120 km within the period between 00:00 and 08:00 on September 3, 2016. Therefore, the T-1612's lowest-density region where the warm core was located was captured at an elevation angle region between 70 mrad and 130 mrad. T-1612 continued to move northwards after 08:00 on September 3, and as a result, the distance between KM and the center of T-1612 was further shortened from 120 km (at 08:00) to 60 km (at 16:00). As a result, the T-1612’s warm core was captured at an elevation angle region between 130 mrad and 200 mrad. Figure 12 shows the resultant muographic image taken between 08:00 and 16:00 on September 3, 2016. In this figure, the image pixels in Fig. 10 were interpolated with polynomial functions. A low-pressure area that is warmer at its center than at its periphery (warm core) is visualized.
Figure 13 compares the eastern azimuthal angle (EAA) (0 < tan φ < 1.0) (Fig. 13A) and western azimuthal angle (WAA) (-1.0 < tan φ < 0) components of the time-sequential muographic data for the 21 days during which T-1908 affected the local atmospheric pressure. The EAA component represents the muons that passed through the atmosphere within the directional range between SSE-SSW, while the WAA component represents those muons that passed through the atmosphere within the direction range between SSW-SWW. In Fig. 13C, the time-dependent BP variations observed at Yakushima and Naze stations are presented for reference31. As illustrated in Fig. 13A, there is an MCR increase event during the period between August 3–8, 2019. This MCR increase event was interpreted as PD associated with T-1908 and is labeled MCR1908 in the current discussion. However, there is no MCR increase event in Fig. 13B between August 3–8. These results are consistent with that PD was observed at Yakushima (south of KM within the directional range between SSE-SSW), but it was not observed at Naze (southwest of KM within the direction range between SSW-SWW) stations.
Figure 14 shows the time-sequential muographic images taken between August 4, and August 8, 2016 to analyze the pressure variations caused by the passage of T-1908. Like previous time-sequential muographic images, the KM's geometrical acceptance and the muon's zenith angular dependence were corrected in this figure. These images were mapped within an elevation angular range between tangents 0–and 1.0, and an azimuthal angular range between tangents ± 1.0. This elevation angular range was respectively equivalent to the horizontal range between 506 km and 20 km at an altitude of 20 km. The overall feature was that the large muon flux region indicated in the reddish pixels in Fig. 13 appeared in the HEA-EAA region between 00:00 and 12:00 on August 6, 2019. This large muon flux region was interpreted as the low barometric pressure (BP) region associated with the T-1908 passage, and these time-dependent BP variations are consistent with the trajectory of T-1908.
In conclusion, gas muography can track meso-beta scale atmospheric density variations. Moreover, since muography measures the near-horizontally integrated density of the atmosphere, and BP stations measure the vertically integrated density of the atmosphere, a three-dimensional image of the atmospheric density distribution can be reconstructed with joint inversion of these techniques. Alternatively, the placement of multiple muographs (multidirectional muography) at dispersed locations could also be used to generate a three-dimensional image of the volume within the viewing angle of these muographs. Each muograph unit is low-cost and versatile, so it is possible to position these units nearly anywhere on land. We anticipate that real-time three-dimensional muographic monitoring of MCS can become practical and widespread in the near future.