## 3 Results
### Remote Sensing Reflectance Model Considering Vertical Distribution Of Phytoplankton
The similar performance of Model A and Model B indicated that adding the contribution of waters between 0.2 m and 0.3 m did not improve the performance of Model A. When a constant term was added to the expression in Model C, the average difference would decrease to below 10%. Model C has a maximum error of \(\sim\)3.5% and an average error of \(\sim\)0.9% for nadir-viewed \(r_{rs}(0^{-})\) in this study. Therefore, for the given optical properties, Model C provided \(r_{rs}(0^{-})\) spectra that closely matched the theoretical values. The parameters of Model C (i.e., \(\mathrm{S_{C1}}\), \(\mathrm{S_{C2}}\), and \(\mathrm{S_{C3}}\)) were listed for five sun zenith angles (i.e., 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), and 75\({}^{\circ}\)) and three wavelengths (i.e., 490, 550, and 675 nm) (Table 3). Notably, the parameters for various light geometries and wavelengths can also be developed, which can then be used to model \(r_{rs}(\lambda,0^{-})\) over a wide range of optical properties. The proposed Model C was validated using the remaining 1/3 Ecolight-simulated data. A comparison between the Ecolight-simulated \(r_{rs}(0^{-})\) and the model-derived \(r_{rs}(0^{-})\) showed that the stratified \(r_{rs}\) model performed well, and only 1.43% of the validation data had APD of \(>\)5%. The average APD was 1.2%, 1.9%, and 1.6% at 490, 550, and 675 nm, respectively (Figure 12). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**0 (\({}^{\circ}\))** & **Parameters** & **490 nm** & **550 nm** & **675 nm** \\ \hline \multirow{3}{*}{15} & \(\mathrm{S_{C1}}\) & 0.0978 & 0.0617 & 0.0758 \\  & \(\mathrm{S_{C2}}\) & 0.0460 & 0.1041 & 0.0836 \\  & \(\mathrm{S_{C3}}\) & \(-\)0.0068 & \(-\)0.0123 & \(-\)0.0067 \\ \hline \multirow{3}{*}{30} & \(\mathrm{S_{C1}}\) & 0.0998 & 0.0644 & 0.0791 \\  & \(\mathrm{S_{C2}}\) & 0.0455 & 0.1023 & 0.0813 \\  & \(\mathrm{S_{C3}}\) & \(-\)0.0067 & \(-\)0.0120 & \(-\)0.0065 \\ \hline \multirow{3}{*}{45} & \(\mathrm{S_{C1}}\) & 0.1034 & 0.0695 & 0.0848 \\  & \(\mathrm{S_{C2}}\) & 0.0443 & 0.0983 & 0.0770 \\  & \(\mathrm{S_{C3}}\) & \(-\)0.0064 & \(-\)0.0114 & \(-\)0.0060 \\ \hline \multirow{3}{*}{60} & \(\mathrm{S_{C1}}\) & 0.1050 & 0.0720 & 0.0879 \\  & \(\mathrm{S_{C2}}\) & 0.0436 & 0.0961 & 0.0744 \\ \cline{1-1}  & \(\mathrm{S_{C3}}\) & \(-\)0.0062 & \(-\)0.0110 & \(-\)0.0058 \\ \hline \multirow{3}{*}{75} & \(\mathrm{S_{C1}}\) & 0.1063 & 0.0746 & 0.0907 \\  & \(\mathrm{S_{C2}}\) & 0.0427 & 0.0930 & 0.0714 \\ \cline{1-1}  & \(\mathrm{S_{C3}}\) & \(-\)0.0059 & \(-\)0.0104 & \(-\)0.0054 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Look up table of model parameters of Model C at different solar zenith angle (\(\theta=15^{\circ},30^{\circ},45^{\circ}\), 60\({}^{\circ}\), and 75\({}^{\circ}\)) at 490, 550, and 675 nm. Figure 11: Performances of Model A, Model B, and Model C: (**a–c**) comparisons between modeled \(r_{rs}(0^{-})\) and Ecolight-simulated \(r_{rs}(0^{-})\) at 490, 550, and 675 nm, respectively; (**d–f**) frequency of \(\Delta r_{rs}(0^{-})\) of different models at 490, 550, and 675 nm, respectively. The Model C was then validated using the field-measured data (N = 9) in Lake Chaohu on 28 May 2013. The model parameters at 490, 550, and 675 nm were obtained from Table 3, according to the sampling location and time of each station. The measured Chl\(a\)(z) profiles, SPIM, \(a_{g}\)(440), and SIOPs were set as the input parameters in Ecolight to derive the Ecolight-simulated \(r_{rs}(0^{-})\) of each sample. The comparison of model-derived \(r_{rs}(0^{-})\) and Ecolight-simulated \(r_{rs}(0^{-})\) indicated that Model C performed well with APD = 2.0%, 2.4%, and 4.1% at 490, 550, and 675 nm, respectively (Figure 13a). The model-derived \(r_{rs}(0^{-})\) was then compared with field-measured \(r_{rs}(0^{-})\), which was derived from field-measured \(R_{rs}(\lambda)\) using the Equation (21) [47].