## 2 Methods
### Measurements and Analysis of Natural Seawater Samples
For each sample the power function fit with a slope parameter, \(\zeta\), was determined using these PSD data over the size range 2-50 \(\upmu\)m. In these determinations, the linear regression analysis was applied to log-transformed data, and the last size bins with very low particle counts were ignored. Although the measured PSDs often showed significant deviations from the power function fits, we use the slope parameter \(\zeta\) as a particle size metric, because this is the most common parameterization of size distribution of marine particles [23; 74]. Additionally, assuming spherical particles, the particle volume distributions were determined from particle number distributions for each sample. From particle volume distributions, we calculated the percentile-based particle diameters such as the median diameter, \(D_{V}^{50}\), and the 90\({}^{\text{th}}\) percentile diameter, \(D_{V}^{90}\). These parameters have been shown to provide potentially useful metrics in the analysis of relationships between the optical and particle size properties in seawater [65]. Measurements and processing of data collected with LISST-VSF for natural seawater samples were made following a protocol similar to that described above for standard polystyrene bead samples. For each experiment, baseline measurements were taken on 0.2 \(\upmu\)m filtered seawater obtained from a given seawater sample. However, a single baseline selected from the lowest measured baselines was used for data processing of all seawater samples to ensure a consistent baseline unaffected by possible variations associated with the imperfect purity of 0.2 \(\upmu\)m filtered seawater prepared during different experiments. To ensure scattering measurements were acquired in a single-scattering regime, samples with an average \(c_{p}\) over 3.0 m\({}^{-1}\) were diluted using 0.2 \(\upmu\)m filtered seawater. Dilution was necessary only for the two most turbid samples collected in the San Diego River Estuary. Between four and eight sets of 50 measurements were collected for each seawater sample with gentle hand mixing between the measurement sets, while a magnetic stir bar was on very low speed changing direction of rotation every 30 s. All results from LISST-VSF measurements for natural seawater samples shown in this paper represent the \(CF_{f}(\psi)\)-corrected volume scattering function of particles, \(\beta_{p}^{LISST}(\psi)\), and \(BF_{f}(\psi)\)-corrected degree of linear polarization of particles, \(DoLP_{p}^{LISST}(\psi)\). For a given sample the final values of \(\beta_{p}^{LISST}(\psi)\) and \(DoLP_{p}^{LISST}(\psi)\) correspond to the median values of the series of measurements that passed the quality control criteria. To determine the particulate scattering, \(b_{p}^{LISST}\), and particulate backscattering, \(b_{bp}^{LISST}\), coefficients, the corrected measured \(\beta_{p}^{LISST}(\psi)\) was first extrapolated in the angular range 150-180\({}^{\circ}\). The extrapolated portion of \(\beta_{p}^{LISST}(\psi)\) was obtained by fitting a specific function to the data of \(\beta_{p}^{LISST}(\psi)\) in the angular range 90-150\({}^{\circ}\). We used two methods for fitting and extrapolating \(\beta_{p}^{LISST}(\psi)\). The first method is based on a non-linear least squares best fit of the analytical function proposed by [PERSON] and [PERSON] [75]. The second method is based on a linear mixing model that finds a non-negative least squares best fit for combined contributions of four end members representing shapes of volume scattering functions associated with scattering by small and large particles, as described in [PERSON] et al. [76].