5:15 PM - 7:15 PM
[PEM10-P26] Simultaneous observation of the time of flight and the Doppler frequency shift of each HF wave refracted in the ionosphere
Keywords:time of flight, Doppler frequency shift, simultaneous observation, ionosonde, cross-correlation, replica
Temporal changes in the time of flight (ToF) of HF waves refracted in the ionosphere have been shown to facilitate the analysis of various ionospheric phenomena, including the equatorial plasma bubble, the traveling ionospheric disturbance, and the propagation of gravity waves. These changes have usually been measured using a continuous Doppler sounding system [1]. However, the process requires further measurement of the ToF, typically accomplished by incorporating of an ionosonde. These two systems operate independently, yielding two distinct sets of values at the time of observation. The correspondence between the two sets is lost. In contrast, it is shown that the ToF and the Doppler frequency shift (DFS) of each HF wave are simultaneously observed using temporally modulated replicas [2]. A simple analysis of two echoes in the F and E regions of the ionosphere is shown below.
The pulse trains transmitted every 6 minutes from the Chung-Li ionosonde in Taiwan [3] were received in Okinawa, Japan from 4:00 to 4:54 on March 24, 2024 (JST). The received samples are then cross-correlated with the model replicas. The resulting amplitudes are plotted on a logarithmic scale as oblique incident ionogram equivalents in Figure 1. The two highest amplitudes of each 4.8 MHz train, which appeared in each of the F and E regions at each observation time (as marked with a red square and a magenta circle, respectively), are further cross-correlated with replicas modulated with frequencies ranging from -2 to 2 Hz to approximate the likelihood functions of the DFS [4]. The maximum likelihood estimates of the DFSs are then used to estimate the change rates of ToFs and their extrapolation during the subsequent 6 minutes of the echoes in the F and E regions, respectively. The observed ToFs of the echoes in the F and E regions are plotted in Figure 2 as a red line with square markers and a magenta line with circle markers, respectively. The one-step extrapolations of the preceding observations are also plotted as a blue line with cross markers and a cyan line with asterisk markers, respectively.
The results show that the one-step extrapolations in the F and E regions, respectively, align with their corresponding ToF values. There is no significant difference between them. It is natural that the estimated changes in ToFs caused by monotonic electron density growth during the local morning show similarity to the observed ToFs at a large time interval. Nonlinear changes in ToFs associated with oscillatory waves or accelerated growth of the instability will be of more interest.
The resolution of the DFS estimate is upper-bounded by the curvature of its log-likelihood function. This bound can be relaxed by increasing the signal-to-noise ratio achieved by transmitting a train of a longer coherent time. The time resolution of the ToF and the DFS estimators is restricted by the interval between transmitted trains of the same frequency. This restriction can be mitigated by using waveforms designed to meet specific resolution requirements. It is expected that more appropriate HF waveforms will allow us to more accurately observe the ToF and DFS of each HF wave for more accurate analysis of the ionosphere.
References:
[1] J. Chum and K. Podolská, “3D Analysis of GW Propagation in the Ionosphere,” Geophysical Research Letters, vol. 45, 2018.
[2] T. Iwamoto and M. Konishi, “Observation of Doppler frequency shift and time of flight of a temporally modulated HF wave propagating through ionosphere,” the Japan Geoscience Union Meeting 2022, Chiba, Japan, May 2022.
[3] K.-J. Ke, C.-L. Su, R.-M. Kuong, H.-C. Chen, H.-S. Lin, P.-H. Chiu, C.-Y. Ko, and Y.-H. Chu, “New Chung-Li Ionosonde in Taiwan: System Description and Preliminary Results,” Remote Sensing, vol. 14, 2022.
[4] T. Iwamoto and M. Konishi, “Estimation of Doppler frequency shift and time of flight of an HF wave transmitted by an ionosonde,” SANE2024-27, IEICE Technical Report, 2024.
The pulse trains transmitted every 6 minutes from the Chung-Li ionosonde in Taiwan [3] were received in Okinawa, Japan from 4:00 to 4:54 on March 24, 2024 (JST). The received samples are then cross-correlated with the model replicas. The resulting amplitudes are plotted on a logarithmic scale as oblique incident ionogram equivalents in Figure 1. The two highest amplitudes of each 4.8 MHz train, which appeared in each of the F and E regions at each observation time (as marked with a red square and a magenta circle, respectively), are further cross-correlated with replicas modulated with frequencies ranging from -2 to 2 Hz to approximate the likelihood functions of the DFS [4]. The maximum likelihood estimates of the DFSs are then used to estimate the change rates of ToFs and their extrapolation during the subsequent 6 minutes of the echoes in the F and E regions, respectively. The observed ToFs of the echoes in the F and E regions are plotted in Figure 2 as a red line with square markers and a magenta line with circle markers, respectively. The one-step extrapolations of the preceding observations are also plotted as a blue line with cross markers and a cyan line with asterisk markers, respectively.
The results show that the one-step extrapolations in the F and E regions, respectively, align with their corresponding ToF values. There is no significant difference between them. It is natural that the estimated changes in ToFs caused by monotonic electron density growth during the local morning show similarity to the observed ToFs at a large time interval. Nonlinear changes in ToFs associated with oscillatory waves or accelerated growth of the instability will be of more interest.
The resolution of the DFS estimate is upper-bounded by the curvature of its log-likelihood function. This bound can be relaxed by increasing the signal-to-noise ratio achieved by transmitting a train of a longer coherent time. The time resolution of the ToF and the DFS estimators is restricted by the interval between transmitted trains of the same frequency. This restriction can be mitigated by using waveforms designed to meet specific resolution requirements. It is expected that more appropriate HF waveforms will allow us to more accurately observe the ToF and DFS of each HF wave for more accurate analysis of the ionosphere.
References:
[1] J. Chum and K. Podolská, “3D Analysis of GW Propagation in the Ionosphere,” Geophysical Research Letters, vol. 45, 2018.
[2] T. Iwamoto and M. Konishi, “Observation of Doppler frequency shift and time of flight of a temporally modulated HF wave propagating through ionosphere,” the Japan Geoscience Union Meeting 2022, Chiba, Japan, May 2022.
[3] K.-J. Ke, C.-L. Su, R.-M. Kuong, H.-C. Chen, H.-S. Lin, P.-H. Chiu, C.-Y. Ko, and Y.-H. Chu, “New Chung-Li Ionosonde in Taiwan: System Description and Preliminary Results,” Remote Sensing, vol. 14, 2022.
[4] T. Iwamoto and M. Konishi, “Estimation of Doppler frequency shift and time of flight of an HF wave transmitted by an ionosonde,” SANE2024-27, IEICE Technical Report, 2024.