# Radon Dynamics in Granite and Calcareous Soils: Long-Term Experiments in a Semi-Arid Context
## 4 Discussion
### Time Series Analyses
#### 4.1.3 Wavelets  
For the granite soil, the results of wavelet analyses confirmed the influence of soil water content, soil temperature, evapotranspiration rate, pressure, and wind speed on radon (Figures 6 and 7), also highlighted in the previous analysis. For the period selected to perform the analysis, important changes in SWC caused a response in radon activity (Figure 7a,b). In the granite soil, rainfalls of November 2021, March-April 2022, and May 2022, which caused an increase in SWC, resulted in an evident increase in radon activity, in all cases occurring simultaneously. Therefore, the individual analysis of both signals established a predominant periodicity from one to several days with the rainfall episodes when they occurred (Figure 7a,b). Within these episodes, SWC and radon activity coincided in the time-frequency domain, showing interrelations explained by cross wavelet transform (XWT) and its wavelet transform coherence (WTC). Furthermore, the effect of pressure and wind variations on radon was also highlighted in the analysis (Figures 6e,f and 7g-j) with marked areas with high common power in the scalograms. These areas are higher in the radon-pressure analysis, indicating a larger influence of these variables [76]. Concerning the influence of soil temperature and ET (Figures 6c,d and 7c-f), the wavelet analysis does not reveal conclusive results, as common areas with strong power (in the case of radon-Soil T or radon-ET) were not detected in the time-frequency domain. For the calcareous soil, wavelet analysis (Figures 6 and 8) identified areas with high common power between pairs of signals, which might be significant in the case of pressure or wind (Figures 6k,l and 8g-j). For these variables, XWT and WTC identify areas of high common power that coincide with the results of the individual analysis of the different signals (Figure 8e,f) in which the different predominant periodicities are established. The scalogram identifies common behaviours between coincident periodicities that exist for these variables and radon. However, SWC's interrelation with radon (XWT; Figure 8a) is weaker compared to granite soil. It appears continuously for the time range in the 64-day period band, but neither in the WTC (Figure 8b) nor in the individual SWC analysis \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{3}{c}{**Principal Component Analysis**} & \multicolumn{3}{c}{**Multiple Linear Regression**} \\ \cline{2-6}  & **PC1** & **PC2** & **B** & **Beta** & \(p\)**-Value** \\ \hline Rn & \(-\)0.499 & 0.320 & \(-\)12,020.20 & & *** \\ Upper SWC & 0.790 & 0.397 & 3982.40 & 0.19 & - \\ Soil T & 0.929 & 0.229 & \(-\)4.19 & \(-\)0.13 & - \\ Wind & 0.096 & \(-\)0.830 & 9.94 & 0.10 & - \\ P & \(-\)0.537 & 0.489 & 12.86 & 0.29 & ** \\ ET & 0.867 & \(-\)0.028 & \(-\)2128.16 & \(-\)0.28 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PCA and MLR of the entire time series at a daily frequency in the calcareous soil. PC corresponds to principal components in the PCA. B and Beta are the coefficients and the standardised coefficients of the MLR, respectively, with their associated \(p\)-value. Significant codes: \(p\)-value: 0 ***\({}^{*}\); 0.01 ***\({}^{*}\); \(>\)0.1 *\({}^{\prime}\). Rn acts as the dependent variable. (Figure 6a). No significant common power areas are identified for soil temperature and ET (Figures 6i,j and 8c-f). Figure 6: Decomposition of the different periodicities for radon (Rn; (**a**,**g**)), soil water content (SWC) (**b**,**h**)), soil temperature (Soil T, (**c**,**i**)), evapotranspiration (ET; (**d**,**j**)), pressure (P; (**e**,**k**)), and Wind (**f**,**l**) of the granite and calcareous soils; spectral strength and coherence range from blue (weak) to yellow (strong) colours. Figure 7: WTC and XWT of the granite soil between \({}^{222}\)Rn and SWC (**a,b**), Soil T (**c,d**), ET (**e,f**), P (**g,h**), and Wind (**i,j**); spectral strength and coherence range from blue (weak) to yellow (strong) colours.