# Radon Dynamics in Granite and Calcareous Soils: Long-Term Experiments in a Semi-Arid Context
## 4 Discussion
### Radon Potential
Radon emanation coefficients can be estimated for any type of soil texture considering a weighted sum of % SSC. Table 5 shows the % SSC for typical clay, silt, foam, and sandy soils. For example, according to Equations (4) and (5), sandy soil has a radon activity of 15.60 kBq m\({}^{-3}\), whereas clay soil has 9.54 kBq m\({}^{-3}\) (for soil with \(\rho_{b}=\) 1.7 g cm\({}^{-3}\) and \(C_{Ra}=\) 50 Bq kg\({}^{-1}\) at 20 \({}^{\circ}\)C). This calculation reveals the strong influence of soil texture on radon activity and how heterogeneities in the soil profile may determine the local radon activity, without considering other crucial aspects such as radon transport and soil hydraulic properties. Furthermore, the influence of temperature on radon activity is negligible compared to soil texture, considering that daily soil temperature variations at a 100 cm depth are less than \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coefficient** & **Clay** & **Silt** & **Sand** \\ \hline \(\varepsilon_{0}\) & 0.10 & 0.14 & 0.18 \\ \(a\) & 1.85 & 1.73 & 1.53 \\ \(b\) & 18.8 & 20.5 & 21.8 \\ \(c\) & 0.012 & 0.01 & 0.011 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fitted parameters and \({}^{222}\)Rn emanation coefficient for clay, silt, and sand [82]. 3 \({}^{\circ}\)C (Figures 2-5). For example, a change from 20 to 30 \({}^{\circ}\)C reduces radon activity from 15.49 to 16.87 kBq m\({}^{-3}\) (for \(C_{Ra}\) = 50 Bq kg\({}^{-1}\) and a loam soil defined in Table 6). However, gas permeability in unsaturated soils is also included in RP and varies significantly with %SSC and SWC. Increasing the water content in soils leads to a decrease in gas permeability, which influences RP, because the presence of water in porous materials decreases both the size of the pores and the effective porosity, and at the same time increases tortuosity [20]. The estimation of the unsaturated gas permeability, \(k_{g}\) (\(S_{w}\)), can be formulated as follows (Equation (6)):  
\[k_{g}(S_{W})=k_{g}(1-S_{W}^{\tau})\cdot\left[1-\left(1-\left(1-S_{W}^{m-1} \right)^{m}\right)^{2}\right], \tag{6}\]  
where \(k_{g}\) is the variable-saturated gas permeability, \(m\) results from the parameter \(n\) of the van Genuchten water retention curve as \(m=1-n^{-1}\), and \(\tau\) is the tortuosity value (commonly \(\tau\) = 0.5) [83]. Applying the approach proposed by [14] for RP studies, \(k_{g}\) and \(n\) are obtained from the Rosetta PTF using %SSC, together with the bulk density of the soil as input variables (Table 5). Figure 9 analyses the impact of water content and soil texture on both radon activity and gas permeability (Figure 9a-c), as well as the radon potential (Figure 9d-f). This comparative analysis contemplates four different soils (clay, silt, loam, and sandy; Table 6) and three different \({}^{226}\)Ra activities, representing soils with low to high radon activity [12]. The calculations considered a bulk density of 1.7 g cm\({}^{-3}\)--a value corresponding to a loam soil--and a porosity of 0.5--an average value of the porosity of a soil--at 20 \({}^{\circ}\)C. Due to the emanation coefficient, radon activity strongly increases from \(S_{w}\) = 0 to 0.1 (SWC = 0.05 for \(\phi\) = 0.5) and remains nearly constant as water saturation increases. Relatively small fluctuations in water content at low values will lead to a high variability in radon concentration, as the long-term radon series also showed (Figures 2 and 3). As previously explained in Section 3.3, this variability is amplified with particle size (i.e., sandy soils). However, the changes in gas permeability are remarkable in clay soils, becoming more impermeable as water saturation increases (resulting in higher \(pk_{g}\) values; Figure 9a-c). Water saturation influences RP evolution by changing radon activity and permeability (Figure 9d-f). As with radon activity, RP reaches its maximum at \(S_{w}\) = 0.1 due to radon emanation.