4.1. Power Variation
 Price and Melnikov  have recently reported the diurnal and seasonal variations of the frequency and power of the first SR mode. A good agreement is found between our FDTD results and the realistic measurements of the first SR mode power variation. As shown in Figure 3, the power variations of the Er and HEW have same patterns, which have two peaks at 0500 and 1400 UT, respectively. The peak at 0500 UT can be explained by day-night terminator effect. Because the receiver is located at 36.0°E, 27.0°N, the sunrise time at that location is approximately at 0400 UT. During sunrise, the ionospheric boundary moves downward because of the solar radiation. Therefore a corresponding increase in the SR power starting from 0400 UT is observed in Figure 3 and reaches its peak at 0500 UT. The second peak in the Er and HEW components at 1400 UT is much stronger than that at 0500 UT, because the lightning activity in the Africa reaches its maximum around 1400 UT. The power variation in the HNS component undergoes different variation pattern in comparison with other two components (Figure 3). Two peaks associated with the lightning activity from Southeast Asia and South America are found around 0900 and 2200 UT. The seasonal power variation is also obviously observed in Figure 3. It is believed that this seasonal variation is related to the seasonal variation of global lighting activity. In April, the lightning activity in Africa is stronger than that in September (see Figure 1). Therefore the corresponding SR power increases in the Er and HEW components around 1500 UT in April are observed. Since the magnitude of the lightning activity in Southeast Asia employed in this paper remains approximately the same in April and September, there is no obvious difference in the SR power at 0900 UT in the HNS component for both seasons. The SR power peak at 2200 UT is stronger in September because of the stronger lightning activity in South America in September. Price and Melnikov  report that the magnitude of SR power at 1400 UT from September to November (SON) is a little stronger than that from March to May (MAM) in the Er component, and remains approximately same in SON and MAM in HEW components. The two peaks in the HNS component around 0800 and 2000 UT in SON are stronger than these in MAM.
 The differences observed between experimental data and FDTD results may be related to fine details of global lightning activity as a function of time employed in FDTD model. The FDTD results are derived from two profiles of global lightning activity (see Figure 1) on the basis of 24-hour averages during 14–21 April 1990 and 2–17 September 1989, respectively [Sentman and Fraser, 1991], while the realistic data [Price and Melnikov, 2004] are based on a 4-year measurement (1999–2003). We can imply from the data presented by Price and Melnikov  that the average magnitude of the lightning activity in Africa from 1999 to 2003 remained approximately the same in MAM and SON, and in Southeast Asia and South America, the magnitude of global lightning in SON was stronger than that in MAM.
 In addition, the relative positions of the three main lightning regions with respect to the receiver also have effects on the power variation in Er, HNS, and HEW components. The source accounting for the lightning activity in Africa is located at 27°E, and is very close to the receiver located at 36°E. Therefore the H field from Africa collected by the receiver is dominated by the east-west component. Meanwhile, the H fields excited by the lightning at Southeast Asia and South America are preferentially in the north-south direction because of the relative positions of the source with respect to the receiver. Therefore two peaks are observed at 0800 and 2200 UT in the HNS component corresponding to the lightning activity peaks in these two regions and a peak associated with the lightning activity in Africa is clearly found at 1500 UT in the HEW component. For the first SR mode, a null of Er component appears at the distance of approximately 10000 km from the source. The sources at Southeast Asia and South America are approximately 8000 km and 11000 km away from the receiver. Because of the null proximity, these two sources contribute much less to the Er component at the receiver than that at Africa, which is only 3000 km from the receiver. Therefore only the peak around 15:00 in Er component is obviously observed.
 Melnikov et al.  reported a terminator effect on Schumann resonances. Here, we employ our FDTD model to describe this effect. Twenty simulations have been performed to calculate the variation of the distribution of the magnitude of the Er component of the first SR mode in the cavity due to the day-night terminator position during a diurnal cycle. The conductivity profiles used in these simulations are the same as we used to obtain the results reported in Figure 3. For illustrative purposes, only one source with the same magnitude is used, which is located at 0°E 0°N, and 40 receivers are positioned on the Earth surface at equal intervals along the equator. Figures 7, 8, 9, and 10 show the variation of the Er distribution of the first SR mode during the 0000 to 2400 UT time interval. The dashed line depicts the position of the day-night terminator at different instants of time. The letters “D” and “N” in the figures mark the day and night regions, respectively. From these 20 plots, it can be seen that the magnitude of the first SR mode is generally stronger during daytime in comparison with nighttime at a fixed position. For example, at longitude 30°, the magnitude of the Er component increases during sunrise, and decreases during sunset, which agrees with what has been previously reported by Melnikov et al. . This variation can be associated with the variation of the ionospheric height. The magnitude of the Er component during daytime is approximately 60% stronger than that during nighttime. We also find that the SR magnitude is stronger when the source is near the day-night terminator (see plots corresponding to 0600 and 1800 UT) than at other times. However, in our FDTD model, we find that the power variations of the first SR mode during the sunrise and sunset are much smaller than those associated with the peaks of the global lightning activity (see Figure 3). This difference can be explained by the different sources used in these two simulations. In Figures 789–10, only one source with constant magnitude is employed. In Figure 3, many sources with different magnitude are used to account for the diurnal variations of the lightning activity at three lightning centers (as described in section 2.2), and the results are in good agreement with the realistic measurements [Price and Melnikov, 2004]. Therefore we believe that the global lightning activity plays a more important role in the variations of the SR power.
Figure 7. Magnitude of the Er component of the electric fields on the surface of the Earth at the equator as a function of longitude. The six plots correspond to different instants of time during the diurnal cycle between 0000 and 0600 UT.
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 The effect of the local time in the SR power is well known. According to Sentman and Fraser  and Melnikov et al. , it can be explained by the variation of the altitude of the ionospheric boundary over an observation point due to solar radiation. Meanwhile, the sources of SR, global lightning activity, tending to maximize at specific universal time in three main lightning regions in a diurnal cycle lead to a corresponding intensification of SR power. Therefore it is believed that the universal time also plays an important role in the variations of SR power. In addition as discussed above, the SR power variations are also influenced by the relative position of the observation point with respect to the main lightning centers, due to the field distribution of SR around the source and the wave orientation.
4.2. Frequency Variation
 The variation of SR frequencies can be explained by mode splitting theory presented by Sentman  due to the asymmetry in the Earth-ionosphere cavity at the day and night sides. The magnitude of the line splitting is in the range of 1.4–1.8 Hz for the cases studied by Sentman . Because of the strong damping in the Earth-ionosphere cavity, the magnitude of the mode splitting is less than or comparable to the inherent width of the lines themselves [Sentman, 1989], which complicates the determination of the eigenfrequencies of the cavity.
 Comparing our FDTD results and data reported by Price and Melnikov , some different features are observed in these two frequency variation patterns (see Figures 4 and 6 and section 3). One of the reasons for this difference may be related to the fact that the frequency variations are averaged over 3 months in the work by Price and Melnikov , while the FDTD results are derived from a model with conductivity profiles corresponding to 15 September 2000 and 15 April 2000. Therefore the difference between these two results can be expected. Another possible reason for this difference is the different methods employed to find the eigenfrequencies. Price and Melnikov  used a Lorentzian function fitting method to derive the eigenfrequencies of the cavity, assuming that there is only one frequency component in each resonance mode. The Lorentzian fitting method is generally suitable for the application in uniform cavity without mode splitting, and an example is presented in our previous work [Yang and Pasko, 2005; Yang et al., 2006]. Sentman  found the maximum magnitude of the first mode splitting to be in the range 1.4–1.8 Hz in realistic measurements. If only one frequency component is used to fit all of the splitting modes, the result will be influenced by the magnitude of all of the splitting modes, and the maximum error can be half splitting range (0.7–0.9 Hz), which can mask the real variation of the resonance frequency. Therefore the Lorentzian function fitting method is not applicable as an accurate method to find the eigenfrequencies of the realistic cavity with mode splitting. In this paper, Prony's method is employed to find the eigenfrequencies of the cavity, by which the mode splitting can be clearly detected. Figure 11 shows the comparison of these two methods for analysis of the HEW component derived from the FDTD model with conductivity profile at 0840 UT on 15 September 2000. The result derived from Prony's method matches the original power spectrum data (solid line in Figure 11) much better than that from the Lorentzian function fitting method (dashed line in Figure 11). By the Lorentzian function fitting method, the first SR frequency is found at 7.45 Hz. By Prony's method, the first SR mode can be found splitting into 7.7 Hz and 7.59 Hz. Because the magnitude of 7.7 Hz mode is much stronger than that of 7.59 Hz mode, we used 7.7 Hz as the first SR frequency to show results presented in Figure 5. A 0.25 Hz difference can be found between these two methods and this difference is close to the magnitude of frequency variations reported by Price and Melnikov .
 Roldugin et al. [2004b] concluded that diurnal SR frequency variation is mainly controlled by local time, and the different field components undergo different variation patterns because of the horizontal inhomogeneity of the ionosphere. Nickolaenko et al.  found that the source area of the global lightning activity also plays an important role affecting the SR frequency variation. We conducted additional simulations (not shown), in which we changed the magnitude of the lightning activity at the three lightning centers, as well as the area and positions of these three lightning centers. We observed the obvious changes of the frequency variation pattern. At a specific time, the mode splitting produced by all of the lightning activity in the cavity is determined by the magnitude of each of the lightning discharges, and their positions with respect to the day-night terminator. With changing the area and the positions of these lightning centers, which determine the positions of the lightning discharges in these centers with respect to the day-night terminator, and the magnitude of these lightning centers, the associated change of the mode splitting leading to the SR frequency variation is expected. Therefore we conclude that the magnitude of the lightning activity in three lightning centers, as well as the area and positions of these three lightning centers are the three main factors controlling the SR frequency variation.