## 4 Results and Discussion  
The proposed statistical modeling approach using UAV-based multispectral imagery aims to perform a rapid and cost-effective valuation of the water eutrophication state by calculating CTSI values quantitatively. So far, the on-site sampling inspection via biochemical analysis in a laboratory has been widely adopted to quantify and validate the pollutant concentrations in official assessments. However, the expensive and time-consuming process is still a significant disadvantage to deal with more urgent and challenging requests from environmental protection and conservation worldwide. The presented method is expected to carry out scientifically sound modeling evaluations with a limited number of biochemical inspection samples, and to provide accurate and timely forecast of the water quality parameters at any position of interest without extensive biochemical inspection tests. We use both multispectrometer and on-site water quality sampling analysis to obtain three sets of water quality parameters on different dates by selecting six different sampling points. Therefore, there are 18 data points available for calculation in statistical and chemical analysis, respectively. However, to verify the accuracy of these regression models, we employ only 12 of these data points at random for regression analysis and the other 6 data points are kept for validation of relevant results obtained from regression models and on-site tests. After the analysis and comparison of the results of a total of 76 regression models, each water quality parameter is able to find the optimal model, which is defined by  
Figure 3: The UAV-based multispectral image from Micsence Altum before calibration (**left**, color bar unit: DN) and after calibration (**right**, color bar unit: reflectance). possessing the largest coefficient of determination (R\({}^{2}\)) that measures how well a statistical model predicts an outcome, i.e., \(0\leq\) R\({}^{2}\)\(\leq\) 1. To conclude the comparison, the band-ratio logarithmic regression model for chlorophyll a, the single-band logarithmic regression model for total phosphorus, the single-band regression model for transparency and the band-ratio logarithmic regression model for dissolved oxygen with specific spectral bands show the largest coefficients of determination, respectively. Table 2 presents the optimal regression equations of the chlorophyll a, total phosphorus, transparency and dissolved oxygen with the reflectance factors of red, red edge and green bands, which are assumed to play the key roles of feature bands in association with the correlated parameters. As shown in Figure 4, the best coefficients of determination (R\({}^{2}\)) of the regression models for chlorophyll a, total phosphorus concentration, transparency and dissolved oxygen were found to be 0.8154, 0.8086, 0.9406 and 0.7339, respectively, which are acceptable for regression analysis and mathematical modeling. The corresponding values of root mean square error (RMSE) for these regression models were 8.5373, 7.9580, 0.0194 and 2.6343, respectively. Among them, particularly, the very small RMSE value in the transparency model reflected excellent precision in data concentration along the line of best fit. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Water Quality** & \multicolumn{2}{c}{**Coefficient of**} \\
**Parameter, (y)** & **Determination (R\({}^{2}\))** & **Optimal Multispectral Regression Model** \\ \hline Chlorophyll a & 0.8154 & \(\mathrm{Ln(y)}=5.8696\times\mathrm{Ln}\Big{(}\frac{N_{RF}}{N_{R}}\Big{)}+2.3998\) \\ \hline Total phosphorus & 0.8086 & \(\mathrm{Ln(y)}=-2.7448\times\mathrm{Ln}(N_{R})-1.3247\) \\ \hline Transparency & 0.9406 & \(\mathrm{(y)}=8.5635\times(N_{R})-0.5747\) \\ \hline Dissolved oxygen & 0.7339 & \(\mathrm{Ln(y)}=-2.3986\times\mathrm{Ln}\Big{(}\frac{N_{RF}}{N_{R}}\Big{)}+3.3716\) \\ \hline \hline \end{tabular}
\end{table}