## 3 Results
### Particle Mass Modelling  
Keeping with the assumption of particle sphericity used in the Mie-based models employed by the FC method, a first attempt of total particle mass calculation for the total, organic and inorganic fractions of the particle population was made as a simple bin-by-bin summation of spherical masses, i.e.,  
\[m_{tot}=\sum_{D,nr}\rho_{nr}V_{D}N_{D,nr}, \tag{9}\]  
where \(\rho_{nr}\) is the apparent density of a particle with real refractive index \(n_{r}\) as defined in Equation (2), \(V_{D}\) is the volume of a sphere of diameter \(D\), \(D\) and \(n_{r}\) are the diameter and real refractive index corresponding to each bin, and \(N_{D,nr}\) is the number concentration of particles within each bin. Given Equation (9) SPM, ISM, and OSM can then be obtained respectively by summing over the entire range of refractive indices or by limiting the summation to real refractive index values above or below the \(n_{r}=1.1\) threshold. The model SPM, ISM, and OSM values produced using this simple particle volume model however grossly overestimated the corresponding UKCW measurements, in certain cases by over two orders of magnitude (Figure 4). A second calculation attempt was therefore carried out using a slightly modified version of the particle volume and total mass model employed in [PERSON] et al. [6]. This model is designed to account for the fractal nature of some marine particles, which can exist as aggregates of smaller units rather than as individuals exclusively, and takes the form  
\[m_{tot}=\sum_{r,nr}\frac{4\pi}{3}\bigg{(}\frac{r}{r_{o}}\bigg{)}^{F(r)}r_{o}^{ 3}\rho_{nr}N_{r,nr}, \tag{10}\]  
where  
\[F(r)=3\bigg{(}\frac{r}{r_{o}}\bigg{)}^{\beta}. \tag{11}\]  
Here it is assumed that the flow cytometer has measured the radius \(r\) of an aggregate particle, which is itself constructed from primary particles of radius \(r_{o}\). \(F(r)\) is known as the fractal dimension of the aggregate. The value of \(r_{o}\) and of exponent \(\beta\) are given as 0.5 \(\upmu\)m and \(-\)0.0533 respectively [33], and for \(r<r_{o}\) the value of \(F\) is fixed at 3. Crucially, the implementation of the model used here substitutes summation for the original integration to reflect the nature of the FC PSDs, extends the original range of 0.25-1000 \(\upmu\)m to the 0.05-2000 \(\upmu\)m range suggested by [PERSON] et al. [23] and implements the effective radius \(r\) directly as half the particle diameter \(D\) determined by the FC method (rather than as the geometric formulation 4/3 \(\times\)\(V/A\) used by [PERSON] et al. [6], where \(A\) is the average projected area). This usage of Mie-derived parameters within a fractal model of mass highlights the dual nature of such modelling procedure: Mie theory is initially employed within the FC method to retrieve an optical size for the particles; the fractal model then reconciles this value with their physical size. Over the extended size range the value of \(F\) was found to vary between 3 (its maximum possible value) and 1.998. The SPM, ISM, and OSM values produced using this fractal procedure were found to model the corresponding UKCW measurements much better than those produced using the simple spherical model, with RMS%E values 57.4%, 148.5%, and 83.1% for SPM, ISM, and OSM respectively (Figure 5). SPM values obtained as the sum of ISM and OSM were found to be close to those derived from the total PSD (RMS%E value 65.2%), indicating that the error introduced by the PSD extension is small. The two Bristol Channel samples, which deviated most obviously from the power law PSD model, produced clear outliers on all three accounts and were not included in the analysis. Median cumulative distributions of SPM, ISM, and OSM were also produced, showing that in a majority of samples 90% of the contribution to all three parameters is from particles between 0.2 and 200 (Figure 6). Figure 4: Comparison of modelled vs. measured **(a)** SPM, **(b)** ISM, and **(c)** OSM values for a simple spherical volume model.