## 4 Discussion  
### Performance of Weighting Average Functions  
The stratified \(r_{rs}\) model was developed by evaluating the weighting average functions and calculating the contribution of each layer to \(r_{rs}(0^{-})\). If the weighting average function did not perform well, the contribution of each layer to \(r_{rs}(0^{-})\) (Equation (8)) and the modeled \(r_{rs}(0^{-})\) would be invalid. Figure 12: Validation of stratified \(r_{rs}\) model using Ecolight-simulated data at (**a**) 490 nm, (**b**) 550 nm, and (**c**) 675 nm at different sun zenith angles (\(\theta\) = 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\)), respectively. Figure 13: Validation of stratified \(r_{rs}\) model using field-measured data (N = 9) of Lake Chaohu on May 28, 2013. Comparison of \(r_{rs}\)-model(0\({}^{-})\) with (**a**) Ecolight-simulated \(r_{rs}\)-EL(0\({}^{-}\)), and (**b**) field-measured \(r_{rs}\)-field(0\({}^{-}\)) at 490, 550, and 675 nm. Note that the model parameters were obtained from Table 3 according to the sampling time and location. In the present study, five combinations of weighting average functions and \(K_{x}\) indicated that \(g_{Z}(K_{d}+K_{Lu})\) achieved the best performance, whereas \(g_{GC}\) and \(g_{S}\) did not perform well, particularly in the green and red wavelengths in highly stratified waters (Figure 7). Moreover, [PERSON] et al. [48] demonstrated that \(g_{GC}\) did not perform well in oceanic waters due to too much weight on the surface layer. The result in this study was also in accordance with the study of [PERSON] and [PERSON] [8], in which the use of \(2K_{d}\) instead of \(K_{d}+K_{Lu}\) in the weighting functions led to minimal errors only (<1%). Gaussian function with maximum values in the water column is often used to describe Chl\(a\)(z) profiles in oceanic waters and deep lakes:  
\[\text{Ch}la(\text{z})=\text{C}_{0}+\frac{h}{\sigma\sqrt{2\pi}}\exp[-\frac{1}{ 2}(\frac{z-z_{\text{max}}}{\sigma})^{2}]. \tag{22}\]  
To discuss the applicability of the stratified \(r_{rs}\) model in waters with different maximum Chl\(a\) depths (\(Z_{\text{max}}\) = 0.0, 0.5, and 1.0 m), the performance of the three weighting average functions (\(g_{Z\text{-}KdKLu}\), \(g_{GC\text{-}KdKLu}\), \(g_{S}\)) in waters was compared (Figure 14). Evidently, \(g_{Z\text{-}KdKLu}\) had lower APD (<5%) than those of \(g_{GC\text{-}KdKLu}\) and \(g_{S}\) in Chl\(a\)(z) profiles with maximum Chl\(a\) at water surface \(Z_{\text{max}}\) = 0.0 m. However, these weighting functions performed worse in waters with maximum Chl\(a\) under water surface \(Z_{\text{max}}\) > 0 m than \(Z_{\text{max}}\) = 0.0 m. For example, APD increased dramatically when \(Z_{\text{max}}\) = 0.5 m and 1.0 m, particularly in the blue spectrum (>10%). The APD in the case of \(Z_{\text{max}}\) = 1.0 m was slightly lower than that of \(Z_{\text{max}}\) = 0.5 m, thereby indicating that the effects of Chl\(a\)(z) vertical profiles on \(R_{rs}\) could be weakened with an increase in \(Z_{\text{max}}\). Overall, the performance of \(g_{Z}(K_{d}+K_{Lu})\) in waters with different \(Z_{\text{max}}\) values verified that the weighting average functions are suitable to shallow eutrophic waters with \(Z_{\text{max}}\) = 0.0 m, but fail in waters with a deep Chl\(a\) maximum layer [49]. \(K_{d}(\lambda,\text{z})\) is very high in the blue region because of the rapid attenuation due to the high content of phytoplankton, NAP, and CDOM in this study. The magnitude and spectrum shape of \(K_{d}(\lambda,\text{z})\) in this study is accordance with the previous studies in turbid productive waters [50; 51; 52]. However, \(K_{d}(\lambda,\text{z})\) has low value in the blue region, and increases to high values in the red and NIR wavelength in clear waters [53; 54]. The relatively high values of \(K_{d}(\lambda,\text{z})\) in the red and NIR region results from the increasing absorption coefficients of pure water in these regions.