# A ROTI-Aided Equatorial Plasma Bubbles Detection Method
## Materials and Methods
### Methods  
The previous IBS method applied the variance of TEC variation to acquire the initial and end times of the EPBs [17]. According to the definition, the ROTI could be seen as the square root of the variance of TEC variation [19]. However, ROTI values are more widely used in monitoring ionospheric irregularities [11; 20; 21]. So, the \"by-product\" of the method in this study, namely the ROTI, is also meaningful.  
The definition of ROTI is the standard deviation of the Rate of TEC (ROT) [19]. ROT at epoch \(t_{i}\) can be computed using the following equation:  
\[ROT(i)=\frac{1}{M(\theta_{i})^{2}}\frac{TEC(i)-TEC(i-1)}{t_{i}-t_{i-1}} \tag{1}\]  
where \(M(\theta)\) is the slant factor depending on satellite elevation (\(\theta\)) suggested by [PERSON] et al. [22]. Ionospheric TEC time series can be computed using the GNSS dual-frequency, geometry-free, combined carrier phase observations for each pair of satellite and receiver [23]. The ROTI over 5 min intervals of ROT data can be calculated as follows:  
\[ROTI=\sqrt{\left\langle ROT^{2}\right\rangle-\left\langle ROT\right\rangle^{2}} \tag{2}\]  
where the notation \(\left\langle\cdot\right\rangle\) is the averaging operation. The unit of ROT and ROTI is TECU per min, where TECU is the unit of TEC (1 TECU = \(10^{16}/\text{m}^{2}\)).  
The ROTI series are then employed to seek the occurrence time of EPBs. Two thresholds, namely \"up threshold\" and \"down threshold\", are adopted. For a period of TEC series (\(T_{1},\ T_{2}\)), if the ROTI values are larger than the down threshold and the maximum values are larger than the up threshold, then this period could have an EPB event. Then, we use the low-order polynomial (third order in this case) to fit the TEC data during (\(T_{1}-7.5\text{ min},\ T_{1}\)) and (\(T_{2},\ T_{2}+7.5\text{ min}\)). That is to say, the TEC data during the event (\(T_{1},\ T_{2}\)) are not used (see Figure 1). We call this strategy the partial fitting, as opposed to the general fitting method. Lastly, the detrended ionospheric TEC series, including possible EPB signals, are extracted by subtracting the fitted TEC series from the observed TEC series. If the TEC depletion maximum (called \"depth\") and duration of the EPB candidate meet the defined thresholds then it can be confirmed as an EPB event or vice versa.  
Table 1 lists the corresponding parameters of the EPBs detection method in this study. The minimums of depth and duration are set to 4 TECU and 10 min, respectively. According to the experimental results, the value of up ROTI could be set to 0.1-0.3 TECU/min (0.2 TECU/min here). The value of down ROTI is very important as it is related to the duration. Figure 2 presents the percent distribution of the ROTI values calculated for station HKKT during 2014. Considering that EPB generally occurs at night, only ROTI values from 6:00-18:00 LT are counted. As shown in Figure 2, the vast majority of the  
ROTI values are smaller than 0.04 TECU/min. Here, the value of down ROTI is set to 0.04 TECU/min. Furthermore, to distinguish from other events which lead not only to TEC depletion but also TEC enhancement (such as MSTIDs), the maximum of detrended TEC should be less than one-third of the depth.