## 3 Results
### Effects of Chl\(a\)(z) Profiles on \(K_{x}\)(\(\lambda\), z)  
The vertical distributions of Chl\(a\)(z) also affected the spectral and vertical variations of \(K_{x}\)(\(\lambda\), z) (Figures 4-6). Similar to vertically homogeneous waters, \(K_{d}\)(\(\lambda\), z) had a similar spectrum shape as \(K_{u}\)(\(\lambda\), z) and \(K_{Lu}\)(\(\lambda\), z), and \(K_{x}\)(\(\lambda\), z) would reach the same asymptotic value when Chl\(a\)(z) profiles became uniform at a great water depth. The \(K_{d}\)(\(\lambda\), z) in the blue range was approximately thrice as that in the green and red bands due to the high content of phytoplankton, NAP, and CDOM (Figure 4a). \(K_{d}\)(\(\lambda\), z) did not exhibit an evident spectral difference among different water depths with less vertical variation of Chl\(a\)(z) (L1 and L2 in Figure 4a,b). However, \(K_{d}\)(\(\lambda\), z) varied considerably from the blue to red wavelengths in seriously stratified waters (L4-L6 in Figure 4d-f). That is, the increase in Chl\(a\) value at a certain depth added to the attenuation of this layer and increased \(K_{x}\). The results showed that the \(K_{d}\)(\(\lambda\), z) spectrum had highest values at z = 0.2 m in waters with low Chl\(a\)(z) vertical variation, but had highest values at z = 0.1 m with large vertical discrepancy in stratified waters (Figure 4). In the highly stratified waters (L4-L6), \(K_{d}\)(\(\lambda\), z) spectrum of deep water (e.g., z = 0.5, 1.0 m) showed weak spectral features in the range of 650 to 700 nm (Figure 4d-f). The \(K_{x}\)(z) profiles at 550 and 675 nm in L1-L6 showed that \(K_{d}\)(\(\lambda\), z) had larger vertical variations than \(K_{u}\)(\(\lambda\), z) and \(K_{Lu}\)(\(\lambda\), z) in highly stratified waters (Figures 5 and 6). Note that the instability of \(K_{x}\)(\(\lambda\), z) near water surface (z = 0.1 m) may be caused by the boundary conditions in the air-water surface. \(K_{d}\)(550, z) had minimal vertical variations and was slightly higher than \(K_{u}\)(550, z) and \(K_{Lu}\)(550, z) under conditions with less vertical variability (L1-L2). However, \(K_{d}\)(550, z) had higher value and larger vertical variability than \(K_{u}\)(550, z) and \(K_{Lu}\)(550, z) in L3-L6, thereby indicating that \(E_{d}\)(550, z) decreased more dramatically than \(E_{u}\)(550, z) and \(L_{u}\)(550, z) in these cases. Compared with  
Figure 3: \(r_{rs}\)(\(\lambda\), z) of Chl\(a\)(z) vertical profiles (L1–L6) at (**a**) 550 and (**b**) 675 nm. G(\(\lambda\), z) of Chl\(a\)(z) vertical profiles (L1–L6) at (**c**) 550 and (**d**) 675 nm. Different lines represent different vertical structure parameters (C\({}_{0}\), h, \(\sigma\)) of Chl\(a\)(z) profiles: L1 (5, 16, 0.6), L2 (10, 16, 0.6), L3 (10, 21, 0.6), L4 (5, 16, 0.2), L5 (10, 16, 0.2), and L6 (10, 21, 0.2). The grey dashed lines represent the corresponding homogeneous cases of the vertical profiles (L1–L6). the asymptotic value, the difference between \(K_{x}\)(550, z) at a depth of 0.2 m and the asymptotic \(K_{x}\)(550, z\({}_{\rm b}\)) value (\(\Delta K_{x}\)(550)) in L6 was 1.59, 0.94, and 1.05 m\({}^{-1}\) for \(K_{d}\), \(K_{u}\), and \(K_{Lu}\), respectively. In addition, compared with vertical homogeneous cases, \(K_{x}\)(550, z) and \(K_{x}\)(675, z) profiles were obvious lower, especially in highly stratified waters. In general, similar to \(\Delta r_{rs}\)(\(\lambda\), z), \(\Delta K_{x}\)(\(\lambda\), z) increased with an increase in h, and decreased with the decrease of \(\sigma\) and C\({}_{0}\). Figure 4: \(K_{d}\)(z) spectrum of Chl\(a\)(z) profiles: (**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 different water depths (z = 0.1, 0.2, 0.3, 0.5, 1.0 m). The inserted figures showed the \(K_{d}\)(\(\lambda\), z) in the range of 550 nm to 700 nm of each Chl\(a\)(z) profiles. “h” represents that the Chl\(a\) value was vertical homogeneous, and the water depth is 0.1 m. “v” represents the vertical inhomogeneous cases.