## 2 Materials and Methods
### Case Study
The tracer was CSSI (carbon chain \({}^{14}\)C to \({}^{34}\)C), and the FingerPro model, as previously described [78; 82], was employed to assess sediment contributions. Integrating the PCA test with the FRN technique enables the estimation of the contributions of the three sources under consideration. Without integration with FRN, determining the source contributions is challenging due to multiple peaks in the distribution. Exclusion of the fruit tree source contributions facilitates identification of the source contributions. The results are presented in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**FP Analysis Details**} & **Integrated Techniques** & **Non-Integrated Techniques** \\ \cline{2-3}  & \multicolumn{2}{c}{**Results**} \\ \hline PCA test & 78\% explained variability & 66\% explained variability \\ \hline Range test & Removed nine tracers & Removed five tracers \\ \hline Goodness of fit & 91\% & 70\% \\ \hline Additional sampling points & \begin{tabular}{c} Included two new points in \\ the analysis \\ (one source, one mixture) \\ \end{tabular} & - \\ \hline Estimated contributions & \
\begin{tabular}{c} 50\% forest \\ 40\% temporary crops \\ 10\% coffee crops \\ \end{tabular} &
\begin{tabular}{c} 80\% forest \\ 15\% temporary crops \\ 5\% coffee crops \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the FingerPro runs for the case of the River Hanabanilla sector. The IH technique, associated with studying the dynamics of surface and underground waters, was applied in the River Hanabanilla sector with periodic measurements of precipitation, wells, springs, and reservoir waters. Isotopic measurements of \({}^{18}\)O and \({}^{2}\)H were conducted, and the geochemical parameters of the water were analyzed as well, allowing the local isotopic line to be obtained. This process also enabled the identification of phenomena (such as evaporation) that deviate from the isotopic behavior of the local line. The isotopic and geochemical data were collected using the FP technique to analyze the water contributions within the reservoir across the three primary basin sectors within the Hanabanilla sub-basin (River Hanabanilla: point II, River Negro: point III, and Charco Azul: point IV). The sources were identified at the discharge point of each sector, and the mixing was taken at the outlet of the reservoir (point I) (Figure 3). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**FP Analysis Details**} & **Integrated Techniques** & **Non-Integrated Techniques** \\ \cline{2-3}  & & **Results** \\ \hline PCA test & 60\% explained variability & 58\% explained variability \\ \hline Range test & Removed one tracer & Removed one tracer \\ \hline Goodness of fit & 86\% & 70\% \\ \hline Additional sampling points & Included two new points in & - \\ according to criteria (+/ \(-\)) & (one source, one mixture) & \\ \hline \multirow{3}{*}{Estimated contributions (sources)} & 50\% forest & 90\% forest \\  & 40\% temporary crops & 10\% coffee crops \\ \cline{1-1}  & 10\% coffee crops & Temporary crops are not \\ \cline{1-1}  & & included \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the FingerPro runs for the case of the River Charco Azul sector. Figure 3: Selected points in the Hanabanilla reservoir used to evaluate water discharge contributions. The initial data's linear discriminant analysis (LDA) shows significant differences between the evaluated sources (II, III, and IV), validating their use for the FP technique. Point I coincides with the end of the discharge of the waters in the dam (coincident with core I taken at the bottom); this point is where all the seas arrive with their mixtures (final mixture). The final source contributions reveal the River Negro sector as the most crucial source with 78%, followed by the River Charco Azul with 15%, and finally, the River Hanabanila with 7%.