## 5 Results
### Accuracy of Numerical Computations
Values of \(n_{i}\) vary between 9.79 \(\times\) 10\({}^{-6}\) and 9.44 \(\times\) 10\({}^{-4}\). The impact of the structural heterogeneity of phytoplankton cells is evaluated by comparison with Lorentz-Mie calculations (particulate assemblages composed of homogeneous spheres only, regardless of the particle group) performed for low and high bulk refractive index. These case studies with homogeneous spheres only are named \"Homogeneous reference cases\". The real and imaginary values of the bulk refractive indices are 1.045 and 9.93 \(\times\) 10\({}^{-4}\) for the \"Homogeneous reference case 1\", 1.043 and 1.36 \(\times\) 10\({}^{-3}\) for the \"Homogeneous reference case 2\", and 1.131 and 1.37 \(\times\) 10\({}^{-4}\) for the \"Homogeneous reference case 3\", respectively (Figure 5b,c). These values of \(n_{r}\) and \(n_{i}\) were chosen to be equal to values of \(n_{r}\) and \(n_{i}\) obtained for the oligotrophic-like, phytoplankton bloom, and the coastal-like case study when \(\xi\) = 4. \"Homogeneous reference cases 1 and 2\" with low \(n_{r}\) represent phytoplankton-dominated Case 1 waters and are compared with the oligotrophic-like and phytoplankton bloom water body, respectively. \"Homogeneous reference case 3\" with high \(n_{r}\) represents mineral-dominated Case 2 waters and is compared with the coastal-like water body. The variation of \(\widetilde{b_{bp}^{a}}\) due to structural heterogeneity of phytoplankton cells is evaluated using the relative absolute difference calculated between the homogeneous reference cases (named  
Figure 4: Results of Lorentz-Mie calculations (DS1) of the particulate backscattering ratio \(\widetilde{b_{bp}^{a}}\) as a function of the hyperbolic slope, \(\xi\), and different values of \(n_{r}\) and N\({}_{\theta}\). The imaginary part of the refractive index = 0.005 as in [PERSON] et al. [5]. This figure can be compared to Figure 1 in [PERSON] et al. [5]. \(x\) in Equation (13)) and oligotrophic, phytoplankton bloom or coastal-like water bodies (named \(y\) in Equation (13)):  
\[\Delta e=\frac{|x-y|}{(x+y)}\times 200\ \left(\%\right) \tag{13}\]  
Figure 5: **(a)** Particulate backscattering ratio \(\widetilde{b_{bp}^{a}}\) as a function of the hyperbolic slope for the oligotrophic-like (red dashed line), phytoplankton bloom (green dashed line), and coastal-like (brown dashed line) water bodies as described in Section 4. Black and gray lines are for homogeneous reference cases. The gray solid line corresponds to \(n_{r}=1.045\), \(n_{i}=9.93\times 10^{-4}\), the black dashed line to \(n_{r}=1.1043\), \(n_{i}=1.36\times 10^{-3}\), and the black solid line to \(n_{r}=1.131\), \(n_{i}=1.37\times 10^{-4}\), respectively. Phytoplankton cells are modeled as two-layered spheres with a relative volume of the cytoplasm of 20% (%cyt-%chl = 80–20). **(b)** as in panel **(a)** but for the real refractive index. **(c)** as in panel **(a)** but for the imaginary part of the refractive index. Even if the numerical relative abundance of phytoplankton is very small for the oligotrophic-like water body (=8.4 \(\times\) 10\({}^{-3}\)%), the structural heterogeneity increases the \(\widetilde{b^{\theta_{s}}_{up}}\) value by 58% compared to the homogeneous case (\"Homogeneous reference case 1\"). This is consistent with previous studies showing the large contribution of coated spheres to the backscattering signal [15; 16; 18; 19; 22; 44]. The value of \(\Delta\epsilon\) calculated between the oligotrophic-like and phytoplankton bloom water bodies is smaller (=22% at \(\xi\) = 4) even if \(\tilde{\mu_{i}}\) is different (9.93 \(\times\) 10\({}^{-4}\) for oligotrophic-like against 1.36 \(\times\) 10\({}^{-3}\) for phytoplankton bloom). This latter pattern provides evidence that the structural heterogeneity (coated-sphere model) has a greater impact on the particulate backscattering ratio than the tested increase in the bulk imaginary refractive index. The relative absolute differences between the phytoplankton bloom and \"Homogeneous reference case 2\" is 41%.