## 2 Methodology  
This work is based on the calculation of time-variable power spectral density (PSD) of the high frequencies (short periods) of Swarm Ne 2 Hz data from LPs, starting from around 65 s. We use wavelengths as frequency domain units, mainly for a better geometrical understanding of the disturbance size found at specific frequency. This unit is derived from the recalculation of Swarm data time units to distances along the orbit, using Swarm speed. It is therefore possible that two frequency domain units are applied alternately, i.e., period and wavelength. However, the term \"period\" is used also in reference to selected time epochs, which can be recognized from the context. The high-pass filtering of selected track parts of Swarm LP data is based on discrete Fourier transform (DFT), which is more universal than wavelets in the band-filtering processes, as it can decompose discrete signals in terms of sinusoids or complex exponentials. The signal of time function x(t) can be decomposed into frequency responses X(\(\omega\)), sampled for the entire \(\omega\) spectrum. These responses can also be transformed back exactly to x(t) via the inverse Fourier transform. The selected signal band can be subtracted from the data, which, contrary to simple methods of detrending, e.g., moving average or polynomial, removes exactly the part of the signal that we want to remove in terms of a frequency band. The nonspectral methods can remove arbitrary frequencies/wavelengths if the signal variances and spectral content differ in different places. The amplitude of signal responses in the frequency domain provides the PSD at individual wavelengths. The amplitude of spectral peaks usually varies with time, and this is the case with Swarm signals recorded along its orbital track. We have to carefully and accurately analyze the time-evolution of ionosphere disturbances measured by Swarm, because the speed of the satellite is fast with respect to sensed disturbances, and therefore, signal samples are composite but short. Time-variable PSDs plotted over time have the ability to map such changes in the frequency domain. The windowed STFT is a modification of the DFT method, which computes the spectrum of overlapping segments of the time series. The output of STFT is the short-term, time-localized evolutionary PSD. The data sequence to be transformed is multiplied using a window function, which is nonzero for only a short period of time [60; 61]. The STFT of the signal is computed as the window is sliding along the time axis, resulting in a two-dimensional representation of the signal. Mathematically, this is written as  
\[STFT_{x,f,t}=\sum_{n=0}^{N-1}x_{n}w_{n-t}W_{N}^{-fn}\qquad f=1,2,\ldots,N-1 \tag{1}\]  
where  
\[W_{N}=e^{\frac{i2\pi}{N}} \tag{2}\]  
and \(w_{n}\) is a discretized window function, and \(t\) is its time index. The window applied in this study is the Tukey window. This window, also known as the cosine-tapered window, can be regarded as a cosine lobe of width \(\frac{r}{2}(N-1)\) that is convolved with a rectangular window of width \(\big{(}1-\frac{r}{2}\big{)}(N-1)\). The equations defining Tukey window are  
\[w_{TU}(n)= \begin{Bmatrix}\frac{1}{2}\Big{[}1+cos\Big{(}\frac{2\pi}{r}\frac{n- 1}{N-1}-\pi\Big{)}\Big{]}&,&n<\frac{r}{2}(N-1)+1\\ 1&,&\frac{r}{2}(N-1)+1\leq n\leq N-\frac{r}{2}(N-1)\\ \frac{1}{2}\Big{[}1+cos\Big{(}\frac{2\pi}{r}-\frac{2\pi}{r}\frac{n-1}{N-1}- \pi\Big{)}\Big{]}&,&N-\frac{r}{2}(N-1)<n\end{Bmatrix}  \tag{3}\]  
where \(r\) is a value between 0 and 1. STFT of a data sequence \(x_{n}\) describes its local spectral content near the moment t as a function of \(f\). Moving the center of the window \(w_{n-t}\) along the real line (of real units) allows for obtaining snapshots of the time-frequency behavior of \(x_{n}\). STFT is used in the calculation of the amplitude of frequency spectrum for each sample. These spectra then form a 2-D shape that depends on the window size and overlay size.