## 3 Results  
### Effects of Chla(z) Profiles on \(r_{rs}(\lambda,z)\)  
The six Chla(z) profiles (L1-L6, Figure 1) were used as examples to illustrate the spectral and vertical variations of \(r_{rs}(\lambda,z)\) in the vertical inhomogeneous waters (Figures 2 and 3). In general, Chla(z) profiles changed the spectrum and magnitude of \(r_{rs}(\lambda,z)\) at different water depths. Compared with \(r_{rs}(\lambda,z)\) in homogeneous waters, \(r_{rs}(\lambda,z)\) considerably increased with water depth and reached the asymptotic value at a certain depth in which Chla(z) became unchangeable. In addition, the spectral variations of \(r_{rs}(\lambda,z)\) in seriously stratified waters were larger than that of Chla(z) profiles with less vertical variations. For example, the difference between \(r_{rs}(\lambda,z)\) at depth z and the asymptotic \(r_{rs}(\lambda,z_{b})\) value (\(\Delta r_{rs}(\lambda,z)\)) of L3-L6 was noticeably larger than that of L1 and L2. \(\Delta r_{rs}(\lambda,z)\) exhibited spectral variations at the green and red wavelengths with a maximum value of approximately 590 nm and showed no evident spectrum shifting of the maximum value (Figure 2). The vertical variations of \(r_{rs}(z)\) were also observed from profiles L1-L6 at 550 nm and 675 nm (Figure 3a,b). A large \(\Delta r_{rs}\) typically occurred at a depth in which Chla(z) exhibited large vertical variations. For example, L1 and L2 achieved the largest variations of Chla(z) and \(\Delta r_{rs}\) at the water depth between 0.5 m and 1.0 m, whereas L4 and L6 obtained the largest \(\Delta r_{rs}\) at the water depth between 0.2 m and 0.5 m. \(\Delta r_{rs}\) is also related to the vertical variation of Chla(z) profiles. For example, the difference of \(r_{rs}\) between 0.1 m and 0.2 m at 550 nm (\(\Delta r_{rs}\)(550, 0.1-0.2)) of L6 was 0.014 sr\({}^{-1}\), whereas the \(\Delta r_{rs}\)(550, 0.1-0.2) of L1 was close to 0.001 sr\({}^{-1}\). In general, \(\Delta r_{rs}(\lambda,z)\) increased with an increase in h and a decrease in \(\sigma\) and C\({}_{0}\). High h and low \(\sigma\) produce high vertical variation of Chla near the water surface, thereby leading to high \(\Delta r_{rs}(\lambda,z)\) (~78%) in L4 and L6. Moreover, the vertical Chla(z) profiles considerably affect \(r_{rs}(z)\) in low background concentration Chla (C\({}_{0}\)). The \(\Delta r_{rs}\) between 0.1 m and 0.2 m of L5-L6 (C\({}_{0}=5\)) was slightly larger than that of L3-L4 (C\({}_{0}=10\)). That is, \(r_{rs}\) will vary substantially in relatively clear waters with large vertical variations of Chla(z). Figure 2: \(r_{rs}\)(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, 0.5, 1.0 m). “h” represents that the Chl\(a\) value was vertical homogeneous, and the water depth is 0.1 m. “v” represents the vertical inhomogeneous cases. \(r_{rs}\)(z) profiles at 550 and 675 nm (grey dash lines) shown in Figure 3a,b. Figure 3: \(Cont.\)  
The \(r_{rs}\)(\(\lambda\), z) profiles exhibited a similar vertical trend with \(b_{b}\)/(\(a+b_{b}\))(\(\lambda\), z), but their ratio [G(\(\lambda\), z) = \(r_{rs}\)(\(\lambda\), z)/(\(b_{b}\)/(\(a+b_{b}\))(\(\lambda\), z))] varied depending on water depth (Figure 3c,d). G(\(\lambda\), z) presented a slight increase in the first layer and then decreased with an increase in depth, particularly in L6 at 675 nm. However, G(\(\lambda\), z) showed minimal vertical variation in cases with low vertical variation of Chl\(a\)(z) profiles, such as in L1-L2. This indicated that G(\(\lambda\), z) contains information of vertical variations between \(r_{rs}\)(\(\lambda\), z) and \(b_{b}\)/(\(a+b_{b}\))(\(\lambda\), z), and the traditional bio-optical remote sensing model (Equation (1)) would not work in stratified waters.