## 3 Results
### Contribution of Each Layer to \(r_{rs}(0^{-})\)
The contribution to \(r_{rs}(0^{-})\) increased with increasing h/\(\sigma\) in the first layer, but slightly decreased with increasing h/\(\sigma\) in the second and third layers. h/\(\sigma\) represents the vertical variation of Ch\(\mathrm{\SIUnitSymbolMicro}\)(z) near the water surface. When h/\(\sigma\) was high, Ch\(\mathrm{\SIUnitSymbolMicro}\)(z) would have noticeably higher value in the first layer, which increased the contribution of this layer. In addition, with increasing C\({}_{0}\), the background value of Ch\(\mathrm{\SIUnitSymbolMicro}\) in the column, the contribution of \(r_{rs}(0^{-})\) increased in the first layer but decreased in the second and third layers. The effects of the structure parameters of the Ch\(\mathrm{\SIUnitSymbolMicro}\)(z) profiles on \(r_{rs}\) contribution varied among different wavelengths and weakened in deep water. Figure 7: Performance of the five combinations of weighting average functions and \(K_{x}\). (**a**) Average relative error of all the simulated data at 490, 550, and 675 nm. Note that 490 nm and 550 nm use the left axis, and 675 nm uses the right axis. Weighting averaged \(r_{rs}\) of (**b**) L1 (5, 16, 0.6), (**c**) L4 (10, 16, 0.2), and (**d**) L6 (10, 21, 0.2) derived by the five weighting average functions. “Z-KdKLu” represents the approach of [PERSON] et al. (2005) using \(K_{d}+K_{Lu}\) in the weighting average function, “Z-2 Kd” represents the approach of [PERSON] et al. (2005) using \(2K_{d}\), “GC-KdKLu” represents the approach of [PERSON] and [PERSON] (1992) using \(K_{d}+K_{Lu}\), “GC-2 Kd” represents the approach of [PERSON] and [PERSON] (1992) using \(2K_{d}\), and “S” represents the approach of [PERSON] and [PERSON] (2011). Take the six Ch\(a\)(z) profiles (L1-L6) as examples, the contribution of each layer to \(r_{rs}\)(0\({}^{-}\)) also varied with different SPIM (ranging from 0 to 60 mg/L) and \(a_{g}\)(440) (ranging from 0 to 4 m\({}^{-1}\)) values (Figure 10). Compared with those of \(a_{g}\)(440), the variations of SPIM considerably influenced the contribution to \(r_{rs}\)(0\({}^{-}\)). In waters with low SPIM, L1 contributed lower than that in waters with high SPIM at the range of 550-700 nm. For example, the contribution of L1 to \(r_{rs}\)(0\({}^{-}\)) increased from 17% to 91% at 490 nm and from 16% to 72% at 550 nm with SPIM increasing from 0 to 60 mg/L. Meanwhile, the contribution of each layer to \(r_{rs}\)(0\({}^{-}\)) had low variations (-5%) with \(a_{g}\)(440) ranging from 0 to 4 m\({}^{-1}\), particularly when SPIM was high. Overall, the contribution of each layer to \(r_{rs}\)(0\({}^{-}\)) varied with water  
Figure 8: Average contribution of each layer to \(r_{rs}\) of simulated data in vertical nonuniform (N = 1008) and uniform waters (N = 1008) at (a) 490, (b) 550, and (c) 675 nm. (d) Take L6 as an example, stacked \(r_{rs}\) contribution of different layers in vertical nonuniform and uniform waters. The dashed lines represent the cases of vertical inhomogeneous water. Figure 9: Contribution of each layer to \(r_{rs}\)(0\({}^{-}\)) on different vertical structure parameters (C\({}_{0}\), h/\(\sigma\)) at z = 0.1, 0.2, 0.3 m: (a) 490 nm, (b) 550 nm, (c) 675 nm. It indicated that the first three layers would contribute about 90% to \(r_{rs}\)(0\({}^{-}\)). depth, wavelength, structure parameters of Chl\(a\)(z) profiles, SPIM, and \(a_{g}\)(440). The contribution to \(r_{\mathrm{rs}}\)(0\({}^{-}\)) varied from 30% to 85% in the first layer, \(\sim\)10-25% in the second layer, and \(\sim\)10% in the third layer. However, one important finding was that the contributions of the first two layers were approximately 80-90% to \(r_{\mathrm{rs}}\)(0\({}^{-}\)) in these waters.