# Radon Dynamics in Granite and Calcareous Soils: Long-Term Experiments in a Semi-Arid Context
## 4 Discussion
### Time Series Analyses  
#### 4.1.1 Statistical Analyses of the Granite Soil  
This analysis considered the detection of discrete events with significant variations in radon activity related to rainfall episodes. The main variables associated with these events are initial radon activity (Rn\({}_{0}\)), maximum radon reached after the rain episode (Rn\({}_{\max}\)), soil water content in the upper soil layer at Rn\({}_{\max}\) (Upper SWC\({}_{\text{Rn max}}\)), pressure at Rn\({}_{\max}\) (\(\text{Pr}_{\text{Rn max}}\)), soil temperature at Rn\({}_{\max}\) (Soil TR\({}_{\text{Rn max}}\)), wind speed at Rn\({}_{\max}\) (Wind\({}_{\text{Rn max}}\)), and accumulated rainfall (Rain). The principal component analysis (PCA) of these variables defined two principal components (PCs), which accounted for 62.3% of the total variance (Table 2). PC1 links Rn\({}_{\max}\) with initial Rn\({}_{0}\), and Rain with Upper SWC\({}_{\text{Rn max}}\). Thus, the Rn\({}_{\max}\) reached after the rain episode depends on the initial radon activity before the rain event. As described previously in Section 3.2, rain mainly defines SWC in the upper soil layer and is the weather factor that affects the most radon variations. PC2 associates weather parameters Wind\({}_{\text{Rn max}}\), \(P_{\text{Rn max}}\) and Soil TR\({}_{\text{Rn max}}\) (similar to air temperature pattern), and they act differently when radon reaches its maximum after the rain episode. Multiple linear regression (MLR) analysis aims to evaluate the significant weight of each variable (acting as independent variables) on the estimation of the maximum radon reached after the rain episode (acting as the dependent variable). In other words, it is a qualitative approach to evaluate which variable affects Rn\({}_{\max}\) the most, rather than providing a predictive equation. The combination of all the variables considered (Table 2) to estimate Rn\({}_{\max}\) leads to an excellent goodness-of-fit, with Pearson's coefficient, R, being 0.816. In the MLR, Rn\({}_{0}\), PR\({}_{\text{Rn max}}\) and Soil TR\({}_{\text{Rn max}}\) can be considered significant variables in the estimation of Rn\({}_{\max}\) (Table 2). This analysis focuses on the variation in radon related \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{2}{c}{**Principal Component Analysis**} & \multicolumn{3}{c}{**Multiple Linear Regression**} \\ \cline{2-6}  & **PC1** & **PC2** & **B** & **Beta** & \(p\)**-Value** \\ \hline Rn\({}_{\max}\) & 0.871 & \(-\)0.007 & 65,674.43 & & * \\ Rain & 0.654 & 0.225 & 77.94 & 0.31 & * \\ Rn\({}_{0}\) & 0.702 & \(-\)0.274 & 0.34 & 0.33 & * \\ Upper SWC\({}_{\text{Rn max}}\) & & 0.161 & \(-\)515.95 & \(-\)0.03 & - \\ P\({}_{\text{Rn max}}\) & \(-\)0.399 & \(-\)0.652 & \(-\)58.84 & \(-\)0.35 & * \\ Wind\({}_{\text{Rn max}}\) & 0.024 & 0.780 & 60.63 & 0.14 & - \\ Soil TR\({}_{\text{Rn max}}\) & \(-\)0.456 & 0.754 & \(-\)88.78 & \(-\)0.43 & * \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Principal component analysis (PCA) and multiple linear regression (MLR) of discrete events with significant variations in radon related to each rainfall episode in the granite 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: 0.05 *\({}^{\prime\prime}\); \(>\)0.1 *\({}^{\prime}\). Rn\({}_{\max}\) acts as the dependent variable. to each rainfall episode in granite soil, where Wind\({}_{\text{Rn max}}\) does not significantly influence Rn\({}_{\text{max}}\) dynamics. Based on these results related to rainfall episodes, we analysed the entire time series at a daily frequency. The dataset contains the following variables: radon activity (Rn), soil water content in the upper soil layer (Upper SWC), soil temperature (Soil T), wind speed (Wind), and pressure (P). Moreover, here, we considered evapotranspiration (ET).