## 2 Data and Methods
### EPB Detection Based on a Local Variance Measure of the Electric Field
We then apply the FIF decomposition and obtain a set of IMCs \(\widehat{E}_{i}(t)\), such that  
\[E(t)=\sum_{i=1}^{M}\widehat{E}_{i}(t)+r(t), \tag{2}\]  
where \(r(t)\) is the residual trend of the decomposition, and \(M\) is the number of extracted IMCs. Figure 3 shows an example of such decomposition. Figure 2: Measurements in the night-side ionosphere by CSES-01 (orbit 7264) of the electron density from LP (**a**) and of the components of the electric field from EFD (**b–d**) in the Cartesian WGS84 reference frame on 26 May 2019 from 03:20 to 03:42 UTC. The crossing of the irregularity by CSES-01 takes place between 03:31 and 03:37 UTC. The third step consists in the calculation of the MWLVM of the set \(\{\widehat{E}_{i}\}\), defined as  
\[\mathrm{V}_{i}^{\mathrm{med}}(t,T_{i})=\frac{\mathrm{V}_{i}(t,T_{i})}{\mathrm{ med}\{\mathrm{V}_{i}(t,T_{i})\}_{t}}, \tag{3}\]  
where \(\mathrm{med}\{\dots\}_{t}\) denotes the median operator and  
\[\mathrm{V}_{i}(t,T_{i})=\frac{1}{N_{i}}\sum_{\tau=t-T_{i}/2}^{t+T_{i}/2}\left( \widehat{E}_{i}(\tau)-\mu_{i}(t,T_{i})\right)^{2} \tag{4}\]  
is the moving variance of \(\widehat{E}_{i}(t)\) over a sliding window of length \(T_{i}\), that corresponds to the length of the kernel function of the low-pass filter used by FIF to extract the \(i\)-th IMC. Here, \(\mu_{i}\) is the moving mean of \(\widehat{E}_{i}\) and \(N_{i}\) is the number of points contained in the time interval \(T_{i}\), i.e., \(N_{i}=T_{i}/dt\), \(dt\) being the sampling time of EFD, in this case \(dt=2\times 10^{-3}\) s (we note that, by design of the FIF decomposition, \(T_{i}\) is always an integer multiple of \(dt\), and so is \(N_{i}\)). The bottom panel of Figure 4 shows a colored contour of \(\mathrm{V}_{i}^{\mathrm{med}}\) obtained from EFD measurements of the reference dataset. The broadband signal due to the presence of the EPB is evident. We then define our activity proxy  
\[\mathrm{V}^{\mathrm{max}}(t)=\max_{T_{i}\in\mathbb{A}}\Bigl{\{}\mathrm{V}_{i} ^{\mathrm{med}}(t,T_{i})\Bigr{\}},\quad\mathbb{A}=[0.006\;\mathrm{s},0.03\; \mathrm{s}]\cup[0.2\;\mathrm{s},0.3\;\mathrm{s}], \tag{5}\]  
where the range \(\mathbb{A}\) (denoted by red horizontal stripes in bottom panel of Figure 4) is chosen so as to retain a spatial accuracy of \(\sim\)2 km (i.e., \(\sim\)0.16\({}^{\circ}\) in latitude) and, at the same time, avoid both spurious systematic signals introduced by the instrument and instrumental/ambient noise at high frequencies. A plot of \(\mathrm{V}^{\mathrm{max}}\) is shown in Figure 4.  
Figure 3: FIF decomposition (see Equation (2)), of \(E(t)\) for the selected interval (see Figure 2). Top left: original field amplitude (blue curve), together with the residual \(r\) from the decomposition (red curve). The other panels show all the IMCs extracted. In total, 20 IMCs were found (from \(\widehat{E}_{1}\) to \(\widehat{E}_{20}\)). The final step of the detection procedure consists in the application of the same clustering algorithm used in [64], but with a few modifications to the parameters employed. More specifically, we set the following:  
1. A threshold of 5000 on the activity proxy \(\mathrm{V^{max}}\);
2. A minimum latitudinal extension of \(1^{\circ}\) for the fluctuations above the threshold;
3. A minimum distance between two consecutive intervals of \(0.4^{\circ}\) (below this value, intervals are merged together). As for the LP detection algorithm (see Section 2.2), the choice of the above values has been made to reduce the percentage of false positives, so as to maximize the performance of the detection. The constraint on the minimum latitudinal extension corresponds to setting a lower limit of roughly 120 km on the size of the interval, while the last constraint means that we consider as the same EPB two intervals which are separated by less than 48 km. The choice of the lower limit ensures, on one hand, that the typical scale size of EPBs [8] is captured by the EFD algorithm.