# Evaluation of the Mid-Latitude Ionospheric trough Using GRACE Data
## 3 Results and Discussion
### Solar Cycle Dependence  
Solar radio flux index F10.7 is used here as a proxy for solar activity conditions. The percentage occurrence of the MIT (i.e., (no. of detected MIT profiles)/(total no. of profiles) \(\times\) 100%) was computed and plotted for each year, as shown in Figure 6. The blue and yellow bars indicate the MIT percentage occurrence for the northern and southern hemispheres, respectively. The red line curve shows the yearly mean variation of F10.7 (see right scale). Comparing the MIT percentage occurrence and F10.7 plots reveals a positive correlation between these two parameters. We found that the occurrence rate of the MIT increases with increased F10.7 values and decreases with decreased F10.7 values. The occurrence rate is approximately 5-20% higher in the southern hemisphere compared to the northern hemisphere throughout the year. The correlation coefficient for F10.7 and MIT percentage occurrence in the southern hemisphere is 0.73, and that in the northern hemisphere is 0.67.  
Figure 7 compares the trough means and minima positions in MLAT and F10.7 for 2002-2015. The yearly average of F10.7 is separately plotted for the northern and southern hemispheres, considering only days for which MIT was detected. Because the MIT is not always simultaneously detected in both hemispheres, the F10.7 average plots do not precisely coincide. Figure 7 shows that the trough minimum location moves poleward  
Figure 5: Polar view of geographic locations of trough minimum locations (red dots) for the northern (**left plot**) and southern (**right plot**) hemispheres. Purple stars show the locations of the geomagnetic pole for each hemisphere.  
Figure 6: Percentage of occurrence of MIT each year in relation to the F10.7 index.  
during low-solar-activity years (2007-2010) and equatorward during high-solar-activity years in both hemispheres. In the northern hemisphere, the dependence on the solar cycle is more pronounced. The results are in agreement with those reported by [PERSON] et al. (2016) ([PERSON] et al., 2016). The trough minimum is observed at approximately 2-4 degrees higher latitude in the northern hemisphere compared to the southern hemisphere.  
The mean and standard deviation (STD) values of trough depth and width were computed for equal-sized F10.7 bins. Figure 8 shows the mean variation in trough depth and width as a function of the F10.7 index. The corresponding STD values are plotted as error bars. We found a clear dependence of the trough depth on the F10.7. The left panel plots show that the trough depth increases with increased F10.7 until it reaches saturation at approximately 200 flux units. A positive correlation between the trough depth and F10.7 increase was also found by [PERSON] et al. (2014), which is caused by dissociative recombination as a result of a high ion temperature correlated with increasing F10.7 levels ([PERSON] et al., 2016). The right panel shows that the mean trough width remains almost constant with the increase in the F10.7 and is larger for the northern hemisphere than the southern hemisphere.  
Figure 8: Variation in depth and width of the mid-latitude trough due to the F10.7 index in the northern and southern hemispheres.  
Figure 7: Solar cycle variation in trough minimum location from 2002 to 2015 for the northern and southern hemispheres.