## 4 Results and Discussion

Table 2: The optimal regression results of chlorophyll a, concentration of total phosphorus, transparency and dissolved oxygen in this study, where \(N_{RE}\) is reflectance of red edge band (717 nm), \(N_{R}\) is reflectance of red band (668 nm) and \(N_{G}\) is reflectance of green band (560 nm). Figure 4: The coefficients of determination of the regression models: (**a**) chlorophyll a, (**b**) total phosphorus concentration, (**c**) transparency and (**d**) dissolved oxygen. Regarding the definition of Carlson trophic state index, it is employed to represent the trophic state of the lake water at a specific sampling position. If the CTSI value calculated is less than 40, it is called oiligotrophic; if 40-50, mesotrophic; if 50-70, eutrophic; and if CTSI is greater than 70, it is called hypereutrophic [36; 37]. The CTSI value was mainly calculated using the following Formula (2), which is a judgment standard that uses multiple parameters to summarize:  
\[\text{CTSI}=\frac{[\text{TSI}(\text{SD})+\text{TSI}(\text{CHL})+\text{TSI}( \text{TP})]}{3} \tag{2}\]  
where SD is the transparency of water measured with the Secchi disk (m), TP is the concentration of total phosphorus in water (ug\(\cdot\)L\({}^{-1}\)) and CHL is the concentration of chlorophyll in water (ug\(\cdot\)L\({}^{-1}\)). The trophic State Indices (TSI) for three environmental parameters were calculated by the following Formulas (3)-(5), respectively [36]. \[\text{TSI}(\text{SD})=60-14.41\times\ln(\text{SD}) \tag{3}\]  
\[\text{TSI}(\text{CHL})=9.81\times\ln(\text{CHL})+30.6 \tag{4}\]  
\[\text{TSI}(\text{TP})=14.42\times\ln(\text{TP})+4.15 \tag{5}\]  
After completing the verification of the water quality parameter regression models, the reflectance after the multispectral image conversion was substituted into the regression equations of the best water quality parameter models to estimate or forecast chlorophyll a, total phosphorus, water transparency and dissolved oxygen at 12 sampling positions in the pond, as shown in Figure 5. The equations for calculating the forecast CTSI value were incorporated and then compared with the real CTSI value calculated through the biochemical analysis results. As shown in Table 3, it was found that the resultant CTSI model demonstrated relatively satisfactory forecast capability, in which the largest CTSI error between the real and predicted CTSI values was 1.4% only at validation point 6, and the RMSE value for all six validation results was as small as 0.6624, strongly indicating that the proposed water quality regression models are favorably feasible for expressing the degree of water eutrophication in terms of CTSI forecast modeling. The CTSI values of six sampling points calculated by either SGS analysis or multispectral regression modeling both revealed a high eutrophic to hypereutrophic state of Sun Moon Pond due to regular human leisure activities and excessive excrement of city animals residing around the pond. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Validation Point**} & **CTSI Calculated by the Regression Model** & **CTSI Calculated from the SGS Data** & **CTSI Error (\%)** \\ \hline
1 & 74.17 & 73.37 & 1.1 \\ \hline
2 & 71.92 & 72.35 & 0.6 \\ \hline
3 & 72.09 & 72.11 & 0.02 \\ \hline
4 & 67.34 & 67.26 & 0.1 \\ \hline
5 & 67.17 & 66.68 & 0.7 \\ \hline
6 & 65.46 & 66.42 & 1.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of Carlson trophic state index (CTSI) values calculated by the regression models and SGS analysis data. Validation points 1–6 were randomly selected from Table 1 for model validation. As previously mentioned, this study aims to explore the CTSI value using the reflectance obtained by the drone equipped with a multispectrometer, and one can use this trophic index to assess the comprehensive trophic state of the water in an ecosystem.