## 2 Data and Methods
### EPB Detection Based on a Local Variance Measure of the Electric Field  
When CSES-01 flies through an equatorial irregularity, the electric field fluctuations increase significantly in a broadband spectrum of frequencies. The observation of such a spread of electric power over a wide range of frequencies is likely generated by the turbulent convection embedded within the plasma depletion; see, e.g., [6; 7; 60; 61; 62; 63]. In Figure 2, we show an example of such a signal recorded by CSES-01 during a crossing of an EPB. In that figure, concurrently with a decrease in the electron density (panel a), an energy increase in the electric field fluctuations is observed in all components (panels b-d). We identify such a multiscale increase as the signature of the crossing of an irregularity by CSES-01. Such a signal shares many similarities with the multifrequency electric field fluctuations observed at auroral latitudes (generated by intense field-aligned currents) that we investigated in [64]. In that work, a new method was devised for the automatic detection of the crossing of the Auroral Oval (AO) by CSES-01 based on the multiscale characterization of the electric field activity. The detection was made by means of a clustering thresholding algorithm applied to a measure of the multiscale relative energy of the electric field. Building on those results, we modified the AO detection algorithm of [64] to allow detecting the crossing of EPBs by CSES-01 by means of electric field measurements only. The modified algorithm relies on Fast Iterative Filtering (FIF) [65] to perform a decomposition of the amplitude of the electric field and uses the Median-Weighted Local Variance Measure (hereafter MWLVM [64]) to calculate a proxy of the electric field activity. FIF is designed to decompose a nonstationary nonlinear signal into a set of Intrinsic Mode Components (IMCs) that oscillate around zero with varying amplitude and frequency, plus a residual or trend. FIF is similar to the Empirical Mode Decomposition (EMD) technique developed by [66], but with an important difference in the calculation of the moving average. Indeed, EMD removes the low-frequency component from a given signal by means of spline interpolation of the signal envelope (defined by the relative extrema of the signal), while FIF convolves the signal with a Fokker-Planck (low-pass) filter function. Such a difference led to the demonstration of the a priori convergence of FIF [67]. Once the proxy  
Figure 1: Automatic detection of the EPB recorded by LP onboard CSES-01 on 18 May 2020, in the night side of orbit 12,716. Blue dots refer to nocturnal density measurements collected by CSES-01. Black dots correspond to the running mean of the density, while plasma depletions, detected by applying thresholds described in Section 2.2, are highlighted by red circles. has been calculated, a clustering algorithm is applied to identify the crossing of the EPB by CSES-01. We refer to the overall procedure as the EFD detection algorithm. The main difference with respect to the original AO detection algorithm [64] is the use of the electric field amplitude as input dataset in place of the full vector electric field (and consequently the use of FIF in place of Multivariate FIF [68]). In the following, other differences will be highlighted if needed. To better describe all the steps of the algorithm, we employ the dataset in Figure 2 as a reference. For any semiorbit in the night-side, we take EFD measurements of the electric field in the Extreme-Low-Frequency (ELF) band, in an equatorial latitudinal band below/above \(\pm\)30\({}^{\circ}\) of quasi-dipole magnetic latitude, and calculate the electric field amplitude \(E(t)=\sqrt{E_{x}^{2}(t)+E_{y}^{2}(t)+E_{z}^{2}(t)}\). Here, we always express all quantities as a function of time \(t\). However, we note that most of the plots use the geographic (or quasi-dipole) latitude in place of \(t\), by exploiting the one-to-one correspondence between the two variables (see Figure 2).