## 4 Discussion  
The modelling of suspended matter parameters for the samples of the UKCW dataset produced an interesting result: PSDs and PRIDs generated using a sphere-based, Mie-derived methodology produced SPM, ISM, and OSM values which compared poorly with their corresponding measured parameters when paired with an equally simple spherical volume model (Figure 4). However, the same PSDs and PRIDs produced comparable results when used directly as inputs for a fractal model of particle volume instead (Figure 5). This reflects two important aspects that should be considered carefully. The first is that the particle diameters found by the FC method are equivalent diameters rather than a direct measure of the physical dimension of the particles strictly [2]. The second is that natural particle populations are not solid spheres, so it is necessary to consider the impact of volume scaling and shape effects on apparent densities. The fractal model effectively rescales apparent particle densities across the size range. This is a feature of dealing with polydisperse natural particle populations that may not be encountered when dealing with effectively monodisperse algal cultures. Application of volume scaling models (Figures 7a and 8) was moderately successful in determining POC and ChIA concentrations, although the variable rate of success between models mirrors the lack of consensus on a single model to accurately represent size-physiology relationships in marine phytoplankton. Indeed, a single set of model parameters is likely to be insufficient to adequately represent the metabolic complexity of all algal organisms [35]. This seems to substantiate the concerns expressed by [PERSON] [19] in noting the large variability between results obtained using different cell volume scaling models. Nevertheless, the further application of an empirical optimization procedure produced good match-ups between modeled and measured POC and ChIA values across the UKCW dataset (Figure 10). Refractive index-based models of \(C_{i}\) and \(Chl_{i}\) were found to require a fractal model of particle volume to produce modelled values comparable with measured ones, particularly in the case of POC (Figure 9). This mirrors the results found for the particle density models for SPM, ISM, and OSM, and suggests that fractal models of volume are necessary to reconcile linear formulations of particle density and intraparticle carbon content with corresponding bulk measurements when natural particle populations with a wide size range and complex composition are involved. The matter is less clear in the case of ChIA, for which the refractive index-based models underestimated measured values in the case of spherical volumes, and even more so in the case of fractal volumes. Since the particle volume model must be consistent between POC and ChIA, we interpret this not as an issue with the fractal approach but rather as a sign that other elements within the overall procedure may be problematic. For example, it is important to remember that the imaginary refractive indices used in the \(Chl_{i}\) estimation represent an approximation based on a single \(n_{i}\) value derived from the literature. A simple optimization procedure shows that the modelled ChIA values of Figure 9b,d are reconciled with the corresponding measured values if \(n_{i}\)(675 nm) = 12.3 \(\times\) 10\({}^{-3}\) and \(n_{i}\)(675 nm) = 11.1 \(\times\) 10\({}^{-3}\) in the fractal volume case and if \(n_{i}\)(675 nm) = 4.2 \(\times\) 10\({}^{-3}\) and \(n_{i}\)(675 nm) = 4.6 \(\times\) 10\({}^{-3}\) in the spherical volume case ([PERSON] [19] and [PERSON] et al. [20] models respectively in both cases). All four values are within the range shown in Table 1 of [PERSON] et al. [36], suggesting that a more dynamic range of \(n_{i}\) values may in fact improve the agreement between measurements and prediction.