## 3 Numerical Modeling of the Marine Particle Scattering  
The Meerhoff Mie program version 3.0 [31] and the ScattnLay code [32; 33] are used to simulate the scattering and absorbing properties of homogeneous and multilayered spheres, respectively. Radiative transfer computations are carried out given the wavelength of the incident radiation equal to 532 nm and the refractive index of sea water equal to 1.34. The Meerhoff Mie program allows simulations of a polydisperse ensemble of spheres with a large choice of PSD. The outputs are the ensemble-average quantities per particle \(\tilde{F}(\theta)\), \(C_{sca}\) and \(C_{sca}^{bb}\) (Equations (2) and (3)). The ScattnLay code performs computations only for monodisperse particles. To obtain the normalized phase function and cross sections for a polydisperse population, a numerical integration over the size range must be done separately (Figure 1, N\({}^{o}\)S2). Particular attention must be paid to the integration step to guarantee the accuracy of the numerical integration. The Meerhoff Mie program is used to generate a first dataset named DS1 based on computations for homogeneous spheres for the same case studies as in [PERSON] et al. [5]. \(n_{r}\) ranges from 1.02 to 1.2 (with a 0.2 increment), \(n_{i}\) is set to 0.005, \(D_{min}\) = 0.012 \(\upmu\)m, \(D_{max}\) = 152 \(\upmu\)m, and \(\tilde{\varsigma}\) is between 2.5 and 5. Please note that [PERSON] et al. [5] did not mix different particle components with different refractive indices, as they studied \(\widetilde{b_{bp}^{\theta_{a}}}\) for a polydisperse population of particles having the same refractive index. In this case, Equations (5)-(7) are not useful as \(\widetilde{b_{bp}^{\theta_{a}}}\) is directly related to \(C_{sca}^{bb}/C_{sca}^{\theta_{a}}\). \begin{table}
\begin{tabular}{c c c c} \hline
**Model \({}^{*}\) (\%cyt-\%chlp)** & **80\%–20\%** & **70\%–30\%** & **80\%–18.5\%–1.5\%** \\ \hline \(n_{r}\) & 1.140 & 1.100 & 1.144 \\ \(n_{i}\) & 6.966 \(\times\)\(10^{-3}\) & 4.688 \(\times\)\(10^{-3}\) & 7.531 \(\times\)\(10^{-3}\) \\ \hline \end{tabular}  
* The percentages represent the relative volume of the model cytoplasm and chloroplast.  
\end{table} 
Table 2: Refractive index (\(n_{r}\)(chlp) + \(i\)\(n_{i}\)(chlp)) of the sphere representing the chloroplast for two morphological models. The refractive index of the sphere representing the cytoplast is constant (1.02 + \(i\) 1.336 \(\times\)\(10^{-4}\)). The equivalent refractive index of the cell is 1.044 + \(i\) 1.5 \(\times\)\(10^{-3}\). of the refractive index of the sphere representing the cytoplasm is fixed to 1.02, and the value of the imaginary part at 532 nm is 1.336 \(\times\) 10\({}^{-4}\)[23]:  
\[n_{i}(\text{cyt},\,532\,\text{nm})=n_{i}(\text{cyt},\,400\,\text{nm})\times \exp[-0.01\times(532-400)] \tag{11}\]  
with \(n_{i}(\text{cyt},\,400\,\text{nm})=0.0005\). Concerning the sphere representing the chloroplast, \(n(\text{chlp})\) is calculated according to the Gladstone and Dale formula [34]:  
\[\sum_{k}n_{k}\times\theta_{k}=n_{equ}, \tag{12}\]  
where \(n_{k}\) and \(\theta_{k}\) are the complex refractive index and the relative volume of the \(k\)-th layer, and \(n_{equ}\) is the complex equivalent refractive index of the whole particle. The knowledge of the complex equivalent refractive index is useful to compare the simulations of heterogeneous spheres among themselves, regardless of the number of layers and the relative proportion of each layer. The complex equivalent refractive index is kept constant (\(n_{equ}=1.044+i\) 1.5 \(\times\) 10\({}^{-3}\)). The refractive index of the sphere representing the chloroplast is described in Table 2 according to the relative volume of the modeled chloroplast (20% or 30%). We also tested a three-layered sphere model. The outer layer represents the cell membrane. We assumed that the cell membrane is non-absorbing and have a \(n_{r}=1.09\)[13]. The second layer represents the chloroplast and the third layer the cytoplasm.