## 3 Results
### Contribution of Each Layer to \(r_{rs}(0^{-})\)  
The contribution of each layer to \(r_{rs}(\lambda\), \(0^{-})\) can be derived using suitable average weighting functions and \(K_{x}(\lambda\), z) profiles based on the average weighting theory. First, the three average weighting functions (i.e., \(g_{CC}\), \(g_{Z}\), and \(g_{S}\), Equations (10)-(12)) were compared to select the \(g_{x}\) function with the best performance in our simulated data. \(K_{d}+K_{Lu}\) was compared with \(2K_{d}\) in \(g_{GC}\) and \(g_{Z}\) due to the large difference between \(K_{d}(\lambda\), z) and \(K_{Lu}(\lambda\), z) in stratified waters. The results indicated that the combination of \(g_{Z}\) with \(K_{d}+K_{Lu}\) achieved relatively better performance in obtaining the weight-averaged \(r_{rs}(\lambda\), \(0^{-})\) (Figure 7a). Notably, the average relative error (RE) between the Ecolight-simulated and weight-averaged \(r_{rs}(\lambda\), \(0^{-})\) derived using \(g_{Z}(K_{d}+K_{Lu})\) was low in 490 nm (\(\sim\)1.2%) and 550 nm (\(\sim\)0.9%), but obviously high in 675 nm (\(\sim\)7.8%). Among all the 1008 simulated data, data with RE \(<\) 2% contributed 82% (827/1008) and 90% (908/1008) in 490 nm and 550 nm, respectively; but data with RE \(>\) 10% were about 21% (208/1008) in 675 nm. Taking L1 as an example, the weight-averaged \(r_{rs}(\lambda\), \(0^{-})\) derived using the five weighting average functions were almost same with the Ecolight-simulated \(r_{rs}(\lambda\), \(0^{-})\), except the wavelength around 675 nm (Figure 7b). It indicated that Ch\(\lambda\) fluorescence affected the accuracy of average weighted \(r_{rs}(\lambda\), \(0^{-})\) around 675 nm. However,  
Figure 6: \(K_{x}(675)\) vertical profiles under different Ch\(\lambda\)(z) distributions: (**a**) L1 (5, 16, 0.6), (**b**) L2 (10, 16, 0.6), (**c**) L3 (10, 21, 0.6), (**d**) L4 (5, 16, 0.2), (**e**) L5 (10, 16, 0.2), and (**f**) L6 (10, 21, 0.2) at 550 nm. \(K_{x}\) represents \(K_{d}\), \(K_{u}\), and \(K_{Lu}\). The solid lines represent the \(K_{x}(675\), z) profiles in vertical inhomogeneous waters (”v”); the dashed lines represent the corresponding cases in vertical homogeneous waters (”h”). the weight-averaged \(r_{rs}(\lambda,0^{-})\) showed a little departure from Ecolight-simulated \(r_{rs}(\lambda,0^{-})\) in highly stratified waters (L4, L6), especially in the wavelength ranging from 550 nm to 700 nm (Figure 7c,d). The weight-averaged \(r_{rs}(\lambda,0^{-})\) derived using \(g_{Z}(K_{d}+K_{Lu})\) was considerably closer to the \(r_{rs}(\lambda,0^{-})\) simulated by Ecolight in L6 (Figure 7d). When \(g_{Z}(K_{d}+K_{Lu})\) was used, the average contribution of each layer to \(r_{rs}(0^{-})\) at 490, 550, and 675 nm generally decreased with water depth and varied at different wavelengths (Figure 8a-c). Overall, layer 1 (0-0.1 m) contributed a noticeably larger budget to \(r_{rs}(0^{-})\) than the second layer (0.1-0.2 m) and the third (0.2-0.3 m), particularly within the blue range. In vertical inhomogeneous waters, the first layer contributed 75% and the second layer contributed 20% in the 490 nm; however, the first layer contributed 50% and the second layer contributed 25% in the 675 nm. That is to say, \(r_{rs}(0^{-})\) contained information from a certain depth, which also varied with wavelength. The contribution of each layer to the \(r_{rs}(0^{-})\) of L6 clearly showed the spectral differences at each layer (Figure 8d). The first two or three layers could dominate \(r_{rs}(0^{-})\) in the blue band, whereas 20% of the contribution would come from water deeper than 0.3 m in the L6 profile. The first two layers (z = 0-0.2 m) of L6 profile contributed more than the vertical uniform case, while, the first three layers (z = 0-0.3 m) had similar contribution in vertical inhomogeneous case and homogeneous case. The contribution of the first three layers to \(r_{rs}(0^{-})\) were then related to the structure parameters (C\({}_{0}\), h/\(\sigma\)) of Ch\(\mathrm{\SIUnitSymbolMicro}\)(z) profiles (Figure 9).