# Evaluation of the Mid-Latitude Ionospheric trough Using GRACE Data
## 2 Database and Method
### Data Processing  
Because the MIT is mainly observed in the 50-70\({}^{\circ}\) geomagnetic latitude region [17], for MIT investigation, we confined our interest to GRACE KBR data distributed in the 40-70\({}^{\circ}\) magnetic latitude regions, covering all longitudes in both the northern and southern hemispheres. Recently [PERSON] et al. (2020) [18] described an algorithm for detecting MIT occurrence using in situ electron density data obtained onboard the three Swarm satellites. Here, we applied a similar technique to the GRACE KBR electron density data and obtained clear signatures of the MIT. For completeness, we described the MIT detection approach below. The detection algorithm consists of the following steps:  
1. We treated Ne data of one satellite passing from the geomagnetic equator to the pole or vice versa as one Ne profile. As previously mentioned, we only considered Ne profile data in the 40-70\({}^{\circ}\) magnetic latitude regions in both hemispheres. Data from other latitude regions (i.e., 40\({}^{\circ}\)S\(-\)40\({}^{\circ}\)N magnetic latitude) were removed from the database. Blue curved lines indicate the MIT search regions in the left plots of Figure 2 for the northern (see top left plot) and southern hemispheres. For geographic to magnetic latitude conversion, we used the International Geomagnetic Reference Field (IGRF) \begin{table}
\begin{tabular}{c c} \hline
**Index** & **Time Resolution** \\ \hline F10.7 & 1 h \\ Solar Wind & 1 h \\ Bx, By, Bz & 1 h \\ Flow pressure & 1 h \\ Hp30 & 30 min \\ SYM-H & 1 min \\ \hline \end{tabular}
\end{table} 
Table 1: Time resolution of space weather indices. Figure 1: Evolution of the orbital altitude during the GRACE mission. model [25]. The red line curves show the where the GRACE satellites pass over the Northern and Southern hemispheres (see Figure 2, left panel plots). 2. The background electron density is calculated as a running average of the Ne in a sliding window of 48 data points. The window size is adapted according to a data resolution equivalent to a horizontal distance of \(\sim\)1800 km. This window size was proven to most optimal. A smaller window size detects some minor irregularities, and a larger window does not properly identify troughs. In Figure 2 (see right panel plots), the background electron density is represented by the black dashed line. 3. We considered \(-0.2\) detrended \(log_{10}\) (Ne) as a threshold value, so if any Ne profile data values fall below the \(-0.2\) level, the profile is identified as an MIT profile. The trough was detected within the detrended logarithmic electron density. The formula is: \[log_{10}\ (Ne)-log_{10}\ (Ne_{MM}),\] (1) where \(Ne_{MM}\) is moving mean with a window size of 48 points. We examined all profiles for negative peaks below the \(-0.2\) level of detrended logarithmic electron density, representing a decrease of about 37% in background electron density. The threshold level was chosen as the most optimal to provide a reliable quality and quantity of detections. 4. If an MIT occurrence is detected in a profile, the next step is to determine the MIT characteristics. Using the Ne profile data, we determined different points/locations, such as the minimum density location or trough minimum (Tm), the equatorward breakpoint (Be), the poleward breakpoint (Bp), the equatorward half point (He), and the poleward half point (Hp) (see Figure 2). The corresponding definitions are provided later in this manuscript. 5. The trough identification quality was verified by applying a trough width filter. The threshold of this criterion was established in a range between \(1^{\circ}\) and \(17^{\circ}\)[6]. Moreover, in assessing the depth of the trough, the range of electron density was assumed to be between \(10^{3}\) and \(10^{5}\) cm\({}^{3}\) to improve the quality of the detection technique, and Ne values outside this limit were considered outliers. Trough width and depth were calculated using the detected Ne values of trough breakpoints and trough minima.