It is well known that the trough structure strongly depends on geomagnetic activity. Herein, we statistically examined the correlation between the Kp index and the trough minimum position. The data with F107 ranges from 100 to 115 solar flux unit (sfu; 1 sfu = 10−22.m−2.Hz−1) were used to study geomagnetic activity dependence. The total number of data points used in the study of geomagnetic activity was 374. The data covered the near-midnight region (2300–0100 MLT). Figure 3 shows a scatter plot of the midnight trough minimum position as a function of the daily Kp index during equinox. The correlation coefficient and the linear regression equation by the least squares method are also shown in the figure. It is clear that a linear correlation is present between the trough minimum position and the Kp index, implying that the day-to-day variability of the trough structure is associated with daily geomagnetic activity. As shown, the trough minimum position moves to a lower latitude as geomagnetic activity increases. Krankowski et al. (2008) showed that the slope of the fitting line for the TEC trough position over Europe as a function of 3h_Kp indices was about 1.0 to 1.6 in January 2005, whereas our results were about 1.8 to 2.0 for the winter season. Karpachev et al. (1996) concluded that the relationship between the trough minimum position and Kp is different at different longitudes. The discrepancy between the slopes is related to the longitudinal effect of the trough minimum position. In addition, the same order of magnitude of the slopes implies that the daily median Kp index is suitable for quantifying the level of geomagnetic activity. Krankowski et al. (2008) showed that the slope of the TEC trough is lower than that of the trough at height of about 550 km, which may be due to the fact that the spatial structure of the trough occurrence depends on height.
Figure 4 shows variations in trough depth, background TEC, and the TEC value at the trough minimum with respect to the daily Kp index during equinox. It can be seen from Fig. 4c that the TEC values at the trough minimum were about 4–5 TECU, regardless of the Kp level. Despite the large scatter of the data in Fig. 4b, there is a trend for the background TEC to increase with increasing Kp. The variation in trough depth with respect to daily Kp index resembles the variation of the background TEC. Rodger et al. (1986) concluded that convection of plasma appears to be the most important process forming the poleward edge of the trough after magnetic midnight when geomagnetic activity is steady or decreasing. Additionally, local particle precipitation may be important when activity is increasing. As such, during periods of enhanced geomagnetic activity, the increase of TEC on the poleward wall in association with local energetic charged particles precipitation results in an increase of the background TEC. In addition, the background TEC is also associated with the TEC value of the equatorward wall, which depends on the positive and negative phases of a storm. Therefore, the correlation coefficient between background TEC and daily Kp is low. A more detailed study of this point would require additional information on the TEC values within the trough wall.
We also investigated the dependence of the trough latitudinal width and the trough half-widths on geomagnetic activity. Figure 5 shows the variation of the trough equatorward half-width, poleward half-width, and width versus daily Kp index during equinox. Figure 5a, c shows that the trough equatorward half-width and the trough width decreased by about 0.57° and 0.7° per unit of Kp, respectively. The correlation coefficient between the poleward half-width and the daily Kp index was very low, which means that there is no linear correlation between them. In addition, the equatorward half-width was correlated with the trough minimum position; the correlation between the two was 0.55. These correlations imply that the trough minimum position and the poleward wall are shifted equatorward more significantly than the equatorward wall as Kp increases. The results are consistent with the findings of Pryse et al. (2006).
In the next section, we examine the dependence of the trough structure on solar activity during three seasons under a low geomagnetic activity level (1.5 ≤ Kp ≤ 2.5). The total number of data points used for the summer, equinox, and winter seasons was 381, 732, and 300, respectively. The data covered the near-midnight region (2300–0100 MLT). Figure 6 shows the variation in trough minimum position with respect to the F107 index during the summer, equinox, and winter seasons. It is clear that the trough minimum position remained unchanged irrespective of the intensity of solar activity. As such, the variation in the trough minimum position is unaffected by solar activity.
In addition to location, trough depth is also of interest, as it may provide clues to the mechanism of trough formation. Figure 7 shows the solar activity variation of trough depth (upper panels), background TEC (middle panels), and TEC value at the trough minimum (lower panels) at a low geomagnetic activity level. The left, middle, and right columns show the results for the summer, equinox, and winter seasons, respectively. The red solid lines represent the piecewise fitting results. As seen in Fig. 7, the increase of TEC with respect to F107 is much steeper at low and moderate F107 values than at high values. The saturation effects in the ionospheric parameters have been reported by many earlier studies (e.g., Balan et al. 1996; Liu et al. 2003; Liu et al. 2006). In order to facilitate the analysis, the fitting lines are shown in Fig. 8. Figure 8 shows that the trough depth, background TEC, and the TEC value at the trough minimum increased with increasing F107 for all seasons. In addition, the correlation between TEC value at the trough minimum and background TEC was about 0.98. It is already known that the loss of electrons is proportional to the electron concentration. Therefore, the increase of background TEC caused by solar activity primarily leads to an increase of trough depth. Some simulations and observational evidence (e.g., Doe et al. 1995 and Nilsson et al. 2005) have indicated a relationship between the F region trough and downward field-aligned currents (FACs). The downward FAC can cause decreased ionospheric densities in the evening sector. Therefore, the region 2 (R2) FAC could possibly play a direct role in the formation of the mid-latitude trough (Lyatsky and Mal’tsev 1981). Ohtani et al. (2014) showed that R2 current is more intense in high solar activity. Therefore, the intensification of the R2 current in high solar activity can also lead to an increase of the trough depth.
In the next section, we examine the diurnal variations of trough structure during three seasons. Median solar activity (90 ≤ F107 ≤ 150) and a low geomagnetic activity level (0.3 ≤ Kp ≤ 2) were selected to ensure the same conditions for each season \( \left(\overline{\mathrm{F}107}=113,\kern0.5em \overline{\mathrm{Kp}}=1.15\right). \) The total number of data points for the summer, equinox, and winter seasons was 186, 142, and 375, respectively. Figure 9 illustrates the MLT variation in the trough minimum position during the summer, equinox, and winter seasons. As illustrated in Fig. 9, the results showed a significant MLT variation in the trough minimum position. The trough minimum position first moves progressively toward lower latitudes, with the lowest latitude around 0400 MLT; it then moves back toward higher latitudes. This result agrees with those found in many earlier studies (e.g., Karpachev et al. 1996; Krankowski et al. 2008; and Lee et al. 2011). It is noteworthy that the range of the trough latitude variation during the dusk-side to morning region (2100–0400 MLT) in summer was larger than the range in other seasons. The trough minimum position decreased with MLT in the pre-midnight to post-midnight region (2000–0400 MLT) sharply in summer and more gradually in winter. In general, the duration of the trough was shorter during summer than that during winter or equinox because of longer exposure to sunlight. In addition, the seasonal variations in trough minimum position differed strongly with different MLT values.
Figure 10 illustrates the MLT variation of trough depth (left panel), background TEC (middle panel), and TEC value at the trough minimum (right panel) in the same manner as Fig. 9. The results show that the trough depth tended to decrease with MLT in the dusk-side (1800–2200 MLT) and morning (0300–0600 MLT) regions, while it increased with MLT in the midnight region (2200–0300 MLT). In the dusk-side region, both the background TEC and the TEC value at the trough minimum decreased with time, but the variation in the background TEC was larger than the variation in the trough minimum TEC, which means the TEC value inside the trough decreases more slowly with MLT than the TEC value outside this region. In the midnight region, the background TEC remained unchanged during summer or equinox, whereas the TEC value at the trough minimum decreased with MLT, which indicates that some mechanisms (e.g., the chemical loss process (Lee et al. 2011)) continue to deplete plasma density in the trough during this period. However, in winter, the background TEC increased with MLT in the midnight region, and the TEC value at the trough minimum changed little with MLT. Rodger (2008) suggested that perhaps several mechanisms that deplete plasma density in the trough may be occurring at the same time, but their relative importance probably changes between events. It is reasonable to suppose that the equatorward wind makes a greater contribution to TEC values in winter. The mid-latitude meridional winds are equatorward through the night and generally peak around 0100–0200 LT (Emmert et al. 2002; Fisher et al. 2015). During winter, the equatorward neutral winds have a more dominant effect in increasing the ionization with MLT than the ordinary ionic recombination in lowering the ionization because of the lower TEC value. A quantitative test of the wind effect in the trough is needed in the future. In the morning region, the trough depth is primarily associated with the scattered solar extreme ultraviolet (EUV) radiation (Schunk et al. 1976).
Finally, the variations of the trough minimum position estimated by the IRI-2007 model were compared with the variations of the GPS-TEC trough minimum position with respect to MLT and F107. The results are shown in Fig. 11. The IRI-TEC trough minimum position is produced by the longitudinal average of the trough minimum positions over 13 longitudes (−180, −150, −120, −90, −60, −30, 0, 30, 60, 90, 120, 150, 180) at the local time. The left and right columns show the results for the IRI-TEC trough and the GPS-TEC trough, respectively. The upper panels show the variation of the trough minimum position with respect to MLT in different seasons at a low geomagnetic activity level. The diurnal variation in the IRI-TEC trough was similar to that of the GPS-TEC trough. However, the IRI-TEC trough was located at higher latitudes. The lower panels show the variation of the midnight trough minimum position with respect to F107 in winter. The GPS-TEC trough minimum position changed little with F107, whereas the IRI-TEC trough minimum position showed a strong F107 dependence. The IRI-TEC did not show any response to geomagnetic activity. However, the trough minimum position depends primarily on geomagnetic activity. The F107 dependence of the IRI-TEC trough minimum position may be affected by the variation of geomagnetic activity. Therefore, the model needs to be further corrected according to geomagnetic activity.