## 3 Results
### Algorithms Retrieval  
In order to find the best algorithms that can estimate TSM, PIM and POM separately, the correlations between the reflectance obtained from the satellite images and the variables measured have been calculated. First, we decided to test the combinations using all the data of the three variables. The regression between the field data and the estimated results were too low (R\({}^{2}<\) 0.3), so we decided to reduce the concentration range of used samples. After various adjustments and tests, the best combinations were extracted for TSM with values lower than 30 mg/L, for POM with values lower than 6 mg/L and for PIM with values lower than 13 mg/L. For all the results, the best fitting function turned out to be the linear adjustment. Once the results are obtained, the ARTMO toolbox provides us their correlation matrices, through a heatmap that indicates the correlation coefficients between the factors in a more visual way, for all possible band combinations. As can be seen in Figures 7 and 8, the correlations presented by the bands, used for developing the different algorithms, positively determine their quality. Figure 6: Correlation between TSM measured in the Jücar and Ebro reservoirs and TSM given by the C2 RCC processor. In blue, line 1:1 is shown. Results relating measured values of these three studied variables and different band combinations, and error statistics results relating measured and estimated values are summarized together in Table 2 (TSM), Table 3 (POM) and Table 4 (PIM). The best 10 results are shown for each variable, these being the ones that presented a higher R\({}^{2}\) and lower RMSE. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Band Comb. (x)**} & \multicolumn{2}{c}{**Formula**} & \multirow{2}{*}{**R\({}^{2}\)**} & \multirow{2}{*}{**RMSE (mg/L)**} & \multirow{2}{*}{**NRMSE (\%)**} \\  & **(y = TSM in mg/L)** & & & \\ \hline
705 & y = 293.06\(\times\) 1.5369 & 0.7918 & 2.7 & 10.3 \\ \hline
783 & y = 454.58\(\times\) 2.7696 & 0.6829 & 3.3 & 12.7 \\ \hline
740 & y = 459.41\(\times\) 2.6277 & 0.6682 & 3.4 & 13.0 \\ \hline
443\(-\)783 & y = \(-\)12.42\(\times\) 13.62 & 0.6377 & 3.6 & 13.6 \\ \hline
490\(-\)783 & y = \(-\)13.51\(\times\) 15.411 & 0.6353 & 3.6 & 13.6 \\ \hline
560\(-\)705 & y = \(-\)13.752\(\times\) 13.585 & 0.6275 & 3.6 & 13.8 \\ \hline
705 & y = 11.407\(\times\) 1.6564 & 0.6169 & 3.7 & 13.9 \\ \hline
441\(-\)865 & y = \(-\)13.947\(\times\) 16.298 & 0.5930 & 3.8 & 14.4 \\ \hline
560\(-\)783 & y = \(-\)15.573\(\times\) 17.901 & 0.5891 & 3.8 & 14.4 \\ \hline
665 & y = \(-\)13.299\(\times\) 3.1289 & 0.5522 & 4.0 & 15.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Algorithm results for TSM. Only the best 10 results are shown. Figure 8: Correlation matrix (measured vs. estimated) for POM using ND (**a**) and SR (**b**) formulations. Yellow combinations are better correlated. Figure 7: Correlation matrix (measured vs. estimated) for TSM using ND (**a**) and SR (**b**) formulations. Yellow combinations are better correlated. Results using only data from 0.6 mg/L to 30 mg/L for TSM, have demonstrated that combining bands located between 443-865 nm the errors obtained between data measured in situ and estimated data are less than 4 mg/L. Even only using the bands located in the red-edge region, this error could be reduced up to 2.7 mg/L. The reflectance in 705 nm (R\({}_{705}\)) is the one that presents the best correlation with the TSM as shown in Figure 9. It is observed that, adjusting by the method of least squares to a linear fitting function, the best adjustment is obtained with the equation:  
\[\text{TSM (mg/L)}=293.06\ \text{R}_{705}+1.5369 \tag{3}\]  
Reservoirs located in the Ebro watershed are those with the lowest amounts of suspended solids, while the Alberta marshes have the highest values. Reservoirs located in the Jucar watershed present more varied values.