## 2 Materials and Methods
With increasing atmospheric pressure (and thus the amount of matter in the air column), the probability of absorption and scattering of particles is increased;
* Decay also demonstrating the negative effect, including the increase in the number of muons decays with increasing atmospheric pressure, which is caused by the increase in the height at which muons are generated;
* Generation defines the positive impact on the muon flux intensity and considers the increase in the number of pions produced with increasing pressure. Near the Earth's surface, the dominant factor is absorption one; considering that air density is usually the highest near the ground, the knowledge of the atmospheric pressure at the level at which the detection is performed is sufficient for determining the value of the barometric effect [12]. Figure 1: The relative positioning of the low-background, digital gamma-ray spectrometer’s detectors. In blue—horizontally (TOP and BOTTOM); in yellow—vertically placed scintillators (FRONT, SIDE and REAR). Each of the scintillators is 5 cm thick. The device is in operation at the Institute of Nuclear Physics Polish Academy of Sciences. Some parts of the passive shield (e.g., the lead walls) are hidden. The normalized deviation of the recorded muon flux from the average depends on the change in atmospheric pressure [13]:  
\[\frac{\Delta I}{I}=\beta_{P}\Delta P, \tag{2}\]  
where \(\frac{\Delta I}{I}\) is the normalized deviation of muon count rate, \(\Delta P\) is the deviation of the atmospheric pressure from the mean and \(\beta_{P}\) is the so-called barometric coefficient. The \(\beta_{P}\) coefficient (expressed in (%/hPa)) can be determined by assuming a linear correlation between changes in the normalized muon flux intensity and variations in atmospheric pressure. Therefore, it is essential to estimate the \(\beta_{P}\) value only during the most geomagnetically quiet days [14]. Pressure corrected data are analyzed using various statistical tools. In order to investigate any correlation between subsequent registered events, the autocorrelation function (ACF) of a sequence of time intervals between pulses generated by detectors is determined. The autocorrelation function indicates the Pearson correlation coefficient between values of the same series as a function of time lag. Furthermore, Fast Fourier Transform (FFT) of a given time series is performed, allowing the investigation of any periodic components. Prior transformation, mean and linear trends have been subtracted from the sequence. In the case of long-period data, a threshold normalization procedure was necessary. The spectrometer's configuration and optimization procedures allow a fixed threshold level for the scintillators spectra to 300 th ADC channel to be set [1]. This procedure allowed redundant data (mainly registered gamma rays) which did not increase the effectiveness of the cosmic ray veto system to be reduced up to around 24 times However, to limit the influence of any signal threshold level fluctuations or gain changes in the digital acquisition circuit which may have occurred in data collected over a long period and cause uncontrolled changes in the recorded number of counts, normalization of the spectra discrimination level was carried out [14]. The normalization procedure involved cutting off part of the energetic spectra located below the ADC channel containing 30% of the maximum number of counts recorded in one channel in a given spectrum (i.e., the highest point in the energy spectrum, see Figure 2). The prepared output files were used to determine a time series of hourly muon count rates for the whole period considered. Figure 2: Scintillator energy spectra discrimination procedure to eliminate fluctuations in the threshold level and signal gain. The black curve is the scintillation detector spectrum with a fixed threshold level set to the 300 th ADC channel; the red dashed line represents 30% of the maximum number of counts registered in one channel in the given spectrum.