## Appendix D Uncertainties  
Uncertainties in satellite radiometry are given in the main text, and model error in terms of uncertainty/variability in the phase function is described fully in [35]. There are many additional sources of uncertainty in the model (non-sphericity of phytoplankton, approximations in sizedistribution, Chlorophyll \(a\) density, to name a few), and further work is needed to quantify them appropriately. For demonstrative purposes here, given that any retrieval of size properties would be performed with the model itself, the model uncertainty is constrained to just that of the phase function variability, as this has a size implication in itself, as shown in [35]. In Figure 10, the model uncertainty is shown for \(R_{rs}\phi\) against a background of total \(R_{rs}\) with nominal additional \(a_{gd}(\lambda)\) and \(b_{nap}(\lambda)\), together with the satellite \(R_{rs}\) measurement uncertainty. Despite the small model uncertainty on the phytoplankton signal in the blue, the huge impact of additional \(a_{gd}(\lambda)\) and the large satellite radiometric uncertainty clearly show the large degree of ambiguity and potential error in the retrieval of the phytoplankton component, even if the \(a_{gd}(\lambda)\) is exactly known. Satellite-derived \(a_{gd}(\lambda)\) (and CDOM) products have large uncertainties: \(r^{2}\) of less than 0.25 for three different \(a_{gd}(\lambda)\) algorithms against in situ data [16]--noting that dependence on the atmospheric correction means that a significant level of error is propagated through the algorithms from this source, particularly in the blue. The most significant spectral regions of Figure 10 in the context of this study are those where the uncertainty on \(R_{rs}\phi\) overlap with the bulk satellite \(R_{rs}\) measurement uncertainty in each example. These are the spectral regions where the phytoplankton-specific signal dominates the bulk signal to the point that they are arguably indistinguishable, so these regions are particularly promising in terms of PFT detection from the bulk \(R_{rs}\). It is also encouraging to note that the regions of maximum \(\delta D_{eff}\) previously identified fall within these regions, meaning that particularly close to 570 nm, the bulk signal not only closely reflects the causal phytoplankton signal but is also not very sensitive to reasonable variability in \(a_{gd}(\lambda)\) and \(b_{nap}(\lambda)\). However, it is an important consideration that these are also regionsof large uncertainty in the size signal, and that, as \(D_{eff}\) increases, the \(R_{rs}\) expression of reduced phytoplankton scatter becomes more vulnerable to variable \(b_{nap}(\lambda)\). At low biomass, the phytoplankton signal falls well outside of the bulk measurement uncertainty, but the question of whether phytoplankton IOPs could be retrieved from the bulk depends on the resulting proportional contribution to the total. With reduced \(b_{b}\phi/a\phi\), even small variability in the non-algal contribution to \(b_{b}/a\) results in signal ambiguity. In this case, the additional \(a_{gd}(\lambda)\) and \(b_{nap}(\lambda)\) contributions need to be exactly known, in order to be able to retrieve any PFT information. It can also be observed in Figure 6 that the magnitude of model uncertainty is less, and the proportional contribution of phytoplankton to the bulk IOPs is greater, at wavelengths slightly shorter than those of the maximum \(\delta D_{eff}\) in the case studies. Thus, the spectral location of the largest observable \(\delta D_{eff}\) signal may not necessarily be the most revealing of PFT discrimination in terms of the associated uncertainties. A sophisticated uncertainty model would be necessary to calculate the respective advantages of reduced contribution uncertainties on a smaller signal vs. slightly larger uncertainties on a larger workable signal. It is also worth considering that, even where the bulk and \(R_{rs}\phi\) signals are distinct, there are spectral regions where they are parallel i.e., maintain the same shape.