## 2 Materials and Method  
For the Case 1 water, whose optical properties are dominated by phytoplankton, the \(\mathrm{R_{rs}}(\lambda)\) in the range of 350-800 nm was simulated using the Hydrolight radiative transfer software [16] with the embedded bio-optical model for Case 1 water [17; 18]. As a numerical forward model, Hydrolight is characterized by its clear physics and faster computation speed, and has been widely used and extensively validated. In the Case 1 bio-optical model, the absorption from pure seawater, phytoplankton, and colored dissolved organic matter, as well as backscattering from pure seawater and phytoplankton was considered. The input chlorophyll a concentrations (Chla) for simulation were 0.01 mg/m\({}^{3}\), 0.03 mg/m\({}^{3}\), 0.1 mg/m\({}^{3}\), 1 mg/m\({}^{3}\), and 10 mg/m\({}^{3}\). The simulated \(\mathrm{R_{rs}}(\lambda)\) is shown in Figure 1.  
For the Case 2 water, R\({}_{\rm rs}\)(\(\lambda\)) data were acquired from observations in turbid waters along the east China coast (\(n=748\)), as shown in Figure 2. The suspended particulate material (SPM) and colored dissolve organic matter (CDOM), rather than phytoplankton, were the dominant ocean color components [19; 20; 21]. For our in situ data, the SPM concentration ranged from 0.10-1762.13 mg/L with an average of 28.30 \(\pm\) 103.85 mg/L. The ranges of CDOM and chlorophyll a concentrations were 0.09-0.42 m\({}^{-1}\) (0.18 \(\pm\) 0.10 m\({}^{-1}\)) and 2.03 \(\pm\) 2.22 mg/m\({}^{3}\) (0.06-14.99 mg/m\({}^{3}\)), respectively. Figure 1: Spectral remote sensing reflectance R\({}_{\rm rs}\)(\(\lambda\)) of Case 1 water, simulated by Hydrolight software under various chlorophyll a concentrations. The overlaid colored areas denote the four bands of CZI (Coastal Zone Imager), whose boundaries are determined by the 1% peak response. Figure 2: Spectral remote sensing reflectance R\({}_{\rm rs}\)(\(\lambda\)) of Case 2 water, measured from turbid coastal waters along the east China coast (\(n=748\)). The overlaid colored areas denote the four CZI bands, whose boundaries are determined by the 1% peak response. The lines of different colors represent the data measured at different stations. For the \(i\)-th band \(\lambda_{i}\), OOB(\(\Delta\)) (difference) and OOB(%) (relative difference) is calculated as follows [14]. \[\text{OOB}(\lambda_{i})(\Delta)\ =\ R_{rs}^{(Total)}(\lambda_{i})-R_{rs}^{(In-Band)}( \lambda_{i}) \tag{1}\]  
where \(R_{rs}^{(Total)}(\lambda_{i})\) and \(R_{rs}^{(In-Band)}(\lambda_{i})\) are the observed total and in-band signals for band \(\lambda_{i}\). \[R_{rs}^{(Total)}(\lambda_{i})\ =\ \frac{\int_{All}R_{rs}(\lambda)F_{0}(\lambda)S_{i} (\lambda)d\lambda}{\int_{All}F_{0}(\lambda)S_{i}(\lambda)d\lambda} \tag{2}\]  
\[R_{rs}^{(In-Band)}(\lambda_{i})\ =\ \frac{\int_{S_{i}(\lambda^{(\pm)})\ =\ 1\%}R_{rs}( \lambda)F_{0}(\lambda)S_{i}(\lambda)d\lambda}{\int_{S_{i}(\lambda^{(\pm)})\ =\ 1\%}F_{0}(\lambda)S_{i}(\lambda)d\lambda} \tag{3}\]  
where \(F_{0}(\lambda)\) is extra-terrestrial incident solar irradiance [22] and \(S_{i}(\lambda)\) is the spectral response function (SRF) for the \(i\)-th CZI band (shown in Figure 3). For the in-band response calculation, the integration is performed over the spectral domain around the peak response from \(\lambda^{(-)}\) corresponding to \(S_{i}\Big{(}\lambda^{(-)}\Big{)}\ =\ 1\%\) to \(\lambda^{(+)}\) corresponding to \(S_{i}\Big{(}\lambda^{(+)}\Big{)}\ =\ 1\%\)[14]. From OOB(\(\lambda_{i})(\Delta)\), the relative out-of-band difference OOB(\(\lambda_{i})(\%)\) can be derived. \[\text{OOB}(\lambda_{i})(\%)\ =\ \frac{\text{OOB}(\lambda_{i})(\Delta)}{R_{rs}^{( In-Band)}(\lambda_{i})}\times 100 \tag{4}\]  
Figure 3: Spectral response functions (SRF, in arb. units) of the two cameras of CZI. The CZI’s wide swath of 950 km is achieved by mosaicking the images acquired by the two cameras, each having 32\({}^{\circ}\) field of view, with 1\({}^{\circ}\) overlapping.