## 2 Materials and Methods
### Atmospheric Data and Methodologies  
The atmosphere was investigated with two types of observables: one is the geomagnetic field, and the other is its composition. The two approaches rely on the different possible main mechanisms that have been previously illustrated in Figure 2.  
The geomagnetic field has been explored with the geomagnetic measurements sampled at 1 min from Guimar (GUI) at Tenerife Island compared with Tamanrasset (TAM) in the Algeria-Sahara Desert, a far observatory from the volcano. GUI is located at 28.321\({}^{\circ}\)N, 16.441\({}^{\circ}\)W, 868 m above sea level and TAM at 22.790\({}^{\circ}\)N, 5.530\({}^{\circ}\)E, 1373 m above sea level. Both observatories are equipped with several instrumentations. Still, in this work, only the fluxgate three components of the geomagnetic field in the NEC (North-East-Centre) frame have been investigated.  
To investigate the atmospheric composition and, in particular, possible alterations due to volcano activity and gas emissions, the data from the climatological archive Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2, [51]) released by NASA and updated monthly were retrieved. The dataset has a spatial resolution of 0.625\({}^{\circ}\) in longitude and 0.5\({}^{\circ}\) in latitude and a time resolution of one hour. For this study, the value closer to the local midnight has been selected to reduce the possible influence of day-time variation produced by solar irradiation on the atmosphere. In particular, solar irradiation increases the Earth's surface temperature, which can facilitate some chemical reactions close to the ground, influencing the atmospheric composition, especially close to the surface, with some of the quantities that we analysed (e.x., CO surface concentration). This paper investigated sulphur dioxide, Dimethyl Sulfide (DMS), Aerosol Optical Thickness (AOT), and carbon monoxide. Volcanoes normally emit such substances, which can be a proxy of the underground activity of magma pressure and movements before the eruptions.  
The values of such parameters in the six months prior to \"La Palma\" volcano eruption were investigated using the \"MErra-2 ANalysis to search Seismic precursors\" (MEANS) algorithm [52]. For each parameter, the algorithm calculates the mean daily value closer to the local midnight not to be influenced by solar irradiation inside a square box of 3\({}^{\circ}\) side centred on the volcano. Then, it compares the value in the year with the eruption with the historical mean and standard deviation of the same day of the other available years from 1980 to 2020 (for example, 23 March 2021 is compared with the mean and standard deviation of (23 March 1980, 23 March 1981,..., 23 March 2020). If one year presents one or more values above the mean + 10 standard deviations, this is excluded, and the whole time series is computed again. This is particularly important for volcano regions to exclude other eruptions that could alter the estimation of the typical value.  
In this paper, we also decided to plot the basic time series of the whole available years from 1980 to the La Palma eruption in 2021. As most of the parameters clearly show a seasonal modulation, the signals have been decomposed by the wavelet decomposition tool of Matlab in several frequencies [53]. For this purpose, we decided to use 9 frequency bands whose limits were selected by the same algorithm based on the spectral energy content in the original signal (as decomposed by wavelet). The reconstructed signal has excluded the frequency band containing a one-year period (i.e., the one with an automatically identified period range from 248 days to 531 days). The detrended (i.e., reconstructed) signal has been analysed as a time series and by the third and fourth statistical moments that estimate the symmetricity and tallness of the distribution--Skewness and Kurtosis.