## 3 Result
### Model Building  
On the basis of the above analysis, linear, quadratic and exponential fittings were performed for the selected 6 band combinations and the measured Chla data, respectively, and 24 different models are fitted, as shown in Table 4. X in Table 4 is the band combination, R\({}^{2}\) is the correlation coefficient and RMSE is the root-mean-square error. Secondary optimization screening was conducted again to select 6 models with high correlation coefficients in the 24 models (underlined in Table 4). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Band Combination(X)** & **Function** & **Fitting Model** & **R\({}^{2}\)** & **RMSE (\(\mu\)g/L)** \\ \hline (P4)/(P3 + P5) & linear & 38.01X \(-\) 14.97 & 0.66 & 1.005 \\ (P4)/(P3 + P5) & quadratic & 443.2X\({}^{2}-347.1X+67.95\) & 0.88 & 0.6102 \\ (P4)/(P3 + P5) & exponential & exp(\(-\)138X\({}^{2}\) + 163.3X \(-\) 45.55) & 0.78 & 0.8685 \\ (P4)/(P3+P5) & exponential & exp(43.36X \(-\) 19.73) & 0.79 & 0.8374 \\ log(P2/P3) & linear & \(-\)22.08X \(+\) 1.287 & 0.42 & 1.3245 \\ log(P2/P3) & quadratic & 262.4X\({}^{2}-29.92X+0.6821\) & 0.58 & 1.1363 \\ log(P2/P3) & exponential & exp(\(22.588X^{2}-33.29X-1.0944\)) & 0.82 & 0.7866 \\ (P3 + P4)/(P2 + P5) & linear & 10.11X \(-\) 9.847 & 0.50 & 1.2230 \\ (P3 + P4)/(P2 + P5) & quadratic & 44.23X\({}^{2}-86.04X+41.73\) & 0.66 & 1.0202 \\ (P3 + P4)/(P2 + P5) & exponential & exp(\(-\)10.159X\({}^{2}\) + 36.408X \(-\) 28.69) & 0.91 & 0.5473 \\ (P3 + P4)/(P2 + P5) & exponential & exp(\(14.32X-16.84\)) & 0.90 & 0.566 \\ (P3 - P4)/(P3 + P4) & linear & \(-\)31.08X \(+\) 8.148 & 0.61 & 1.0893 \\ (P3 - P4)/(P3 + P4) & quadratic & 314X\({}^{2}-163X+21.23\) & 0.81 & 0.7623 \\ (P3 - P4)/(P3 + P4) & exponential & exp(\(-\)42.755X\({}^{2}-14.195X+4.0796\)) & 0.58 & 1.1882 \\ (P3 - P4)/(P3 + P4) & exponential & exp(\(-\)32.16X \(+\) 5.861) & 0.58 & 1.1851 \\ (P2 - P4)/(P2 + P4) & linear & \(-\)16.88X \(+\) 5.154 & 0.68 & 0.9836 \\ (P2 - P4)/(P2 + P4) & quadratic & 104.5X \(-\) 63.29X \(+\) 9.459 & 0.95 & 0.4051 \\ (P2 - P4)/(P2 + P4) & exponential & exp(\(-\)32.588X\({}^{2}\)-6.5659X \(+\) 2.3315) & 0.97 & 0.3317 \\ (P2 - P4)/(P2 + P4) & exponential & exp(\(-\)21.03X \(+\) 3.673) & 0.94 & 0.4322 \\ (P5 - P4)/(P2 + P3) & linear & \(-\)33.52X \(-\) 1.268 & 0.51 & 1.2139 \\ (P5 - P4)/(P2 + P3) & quadratic & 599X\({}^{2}\) + 48.14X \(+\) 0.7035 & 0.81 & 0.758 \\ (P5 - P4)/(P2 + P3) & exponential & exp(\(131.95X^{2}-26.229X-4.0486\)) & 0.81 & 0.8062 \\ (P5 - P4)/(P2 + P3) & exponential & exp(\(-\)44.22X \(-\) 4.483) & 0.80 & 0.8279 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: 24 Models of six band combinations and the corresponding correlation coefficients (R\({}^{2}\)) and root-mean-square error (RMSE). Figure 3: Band combined image of 2 September 2019. (**a**): The grayscale image of band combination P4/(P3 + P5);(**b**): The grayscale image of band combination log(P2/P3); (**c**): The grayscale image of band combination (P3 + P4)/(P2 + P5); (**d**): The grayscale image of band combination (P3 - P4)/(P3 + P4), (**e**): The grayscale image of band combination (P2 - P4)/(P2 + P4); (**f**): The grayscale image of band combination (P5 - P4)/(P2 + P3). The fitting results with a high correlation coefficient of 6 models in Table 4 are shown in the Figure 4a-f correspond to the band combinations in Table 4. It can be seen from the correlation analysis in Figure 4 that the correlation coefficient of the exponential fitting form model of band combination (P2 - P4)/(P2 + P4) is the largest. Figure 4: Curve fitting results of 6 models. The abscissa represents the combination ratio of band reflectivity. The ordinate in Figure 4b,c,e is the natural log of the measured data (Ln(Chla)), and the ordinate in Figure 4a,d,f is the measured data for Chla.