## 2 Data and Methods
### Pigment Retrieval from \(R_{\text{rs}}(\lambda)\)  
#### 2.5.1 \(a_{\text{Gau}}(\lambda)\) from \(R_{\text{rs}}(\lambda)\)  
The multi-pigment inversion model (MuPI) was used to retrieve \(a_{\text{Gau}}(\lambda)\) from \(R_{\text{rs}}(\lambda)\). [PERSON] et al. [63; 73] developed this semi-analytical inversion model (MuPI) to retrieve \(a_{\text{Gau}}(\lambda)\) from hyper- or multi-spectral \(R_{\text{rs}}(\lambda)\). A brief description of MuPI is presented here. The functional \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Peak** & **Pigments** & **Peak\_loc (nm)** & **Width(FWHM) (nm)** & **Relationships** & \(\mathbf{R^{2}}\) \\ \hline
1 & Chl-a & 406 & 16 & 1.13x\({}_{1}\)\({}^{1.01}\) & 0.98 \\
2 & Chl-a & 434 & 12 & \(x_{1}\) & – \\
3 & Chl-c & 453 & 12 & 0.60x\({}_{1}\)\({}^{0.95}\) & 0.99 \\
4 & Chl-b & 470 & 13 & 0.51x\({}_{1}\)\({}^{0.97}\) & 0.98 \\
5 & PPC & 492 & 16 & \(x_{2}\) & – \\
6 & PSC & 523 & 14 & 0.87x\({}_{2}\)\({}^{1.17}\) & 0.99 \\
7 & PE & 550 & 14 & 0.79x\({}_{2}\)\({}^{1.27}\) & 0.96 \\
8 & Chl-c & 584 & 16 & 0.40x\({}_{2}\)\({}^{1.17}\) & 0.96 \\
9 & PC & 617 & 13 & 0.34x\({}_{1}\)\({}^{1.14}\) & 0.93 \\
10 & Chl-c & 638 & 11 & 0.47x\({}_{2}\)\({}^{1.19}\) & 0.96 \\
11 & Chl-b & 660 & 11 & 0.30x\({}_{2}\)\({}^{1.11}\) & 0.94 \\
12 & Chl-a & 675 & 10 & 0.86x\({}_{1}\)\({}^{1.11}\) & 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The 12 Gaussian curves corresponding to the phytoplankton pigment absorption coefficients, with Peak_loc as the center location of each pigment absorption peak and width as the full width at half maximum (FWHM). The relationships indicate the power-law relationships used to estimate the Gaussian peak amplitudes from the two independent variables: \(x_{1}\): \(a_{\text{Gau}}(434)\) and \(x_{2}\): \(a_{\text{Gau}}(492)\). Chl-a: chlorophyll \(a\), Chl-b: chlorophyll \(b\), Chl-c: chlorophyll \(c\), PPC: photo-protective carotenoids, PSC: photosynthetic carotenoids, PE: phycoerythrin and PC: phycoocyanin. relationship between \(R_{\text{rs}}(\lambda)\) and inherent optical properties (IOPs) is taken from [PERSON] et al. [47] and [PERSON] et al. [49]:  
\[R_{\text{rs}}(\lambda)=0.52{\sum_{i=1}^{2}g_{i}\bigg{[}\frac{b_{\text{b}}( \lambda)}{a(\lambda)+b_{\text{b}}(\lambda)}\bigg{]}^{i}}/\Bigg{\{}1-1.7{\sum_{i=1 }^{2}g_{i}\bigg{[}\frac{b_{\text{b}}(\lambda)}{a(\lambda)+b_{\text{b}}(\lambda) }\bigg{]}^{i}\Bigg{\}} \tag{2}\]  
where \(g_{1}\) (sr\({}^{-1}\)) and \(g_{2}\) (sr\({}^{-1}\)) are fixed to 0.089 and 0.125 sr\({}^{-1}\). The IOP spectra, \(a(\lambda)\) and \(b_{\text{b}}(\lambda)\), are partitioned into relevant components  
\[b_{\text{b}}(\lambda)=b_{\text{bw}}(\lambda)+b_{\text{bp}}(\lambda) \tag{3}\]  
\[a(\lambda)=a_{\text{w}}(\lambda)+a_{\text{ph}}(\lambda)+a_{\text{dg}}(\lambda) \tag{4}\]  
with \(b_{\text{bw}}(\lambda)\) for seawater backscattering coefficient [74] and \(a_{\text{w}}(\lambda)\) for seawater absorption coefficient [75; 76]. Phytoplankton absorption coefficient (\(a_{\text{ph}}(\lambda)\)) is modeled following Equation (1); \(b_{\text{bp}}(\lambda)\), particulate backscattering coefficient, is modeled following Equations (5) and (6) [49]; and the combined dissolved and detrital particulate absorption coefficient \(a_{\text{dg}}(\lambda)\) is modeled using Equation (7) [77; 52; 78]. \[b_{\text{bp}}=b_{\text{bp}}(\lambda_{0})\bigg{(}\frac{\lambda_{0}}{\lambda} \bigg{)}^{\eta} \tag{5}\]  
\[\eta=2\bigg{(}1-1.2\exp\bigg{(}-0.9\frac{R_{\text{rs}}(440)}{R_{\text{rs}}(55 0)}\bigg{)}\bigg{)} \tag{6}\]  
\[a_{\text{dg}}(\lambda)=a_{\text{dg}}(\lambda_{0})\exp(-S(\lambda-\lambda_{0})) \tag{7}\]  
where \(\lambda_{0}\) is a reference wavelength (nearest to 440 nm), \(S\) is the spectral decay constant for absorption of detrital and dissolved materials and kept as an unknown within 0.007 to 0.02 nm\({}^{-1}\)[77; 52; 78]. \(\eta\) is the power-law exponent for the particulate backscattering coefficient calculated from the \(R_{\text{rs}}(440)\) to \(R_{\text{rs}}(550)\) ratio following [PERSON] et al. [49].