## 3 Results
### Particulate Organic Carbon and Chlorophyll-a Concentration Modelling  
For POC and ChlA modelling, the particle volume \(V\) was once again defined using a simple spherical model. The first to be applied were the cell volume scaling models (Table 2). Of the four models used to calculate POC values, only the diatom model given by [PERSON] and [PERSON] (2008) produced results compatible with POC measurements (RMS%E: 92.9%, Figure 7a). This possibly reflects the taxonomical composition of the algal populations encountered during the He442 research cruise being mainly composed of diatom species typically associated with the spring bloom. The median cumulative distribution of POC for the diatom model shows an almost linear contribution from all size classes in a majority of samples, although results are shown to range widely from cases where the contribution is dominated by small particles to cases where, oppositely, the largest particles contributed the most (Figure 7b). This is likely the result of the interaction between the model parameters and the slope of the PSDs, and may also indicate that the parameters of the model work well for a majority, but not all of the samples. The two chlorophyll-a models both produced unsatisfactory results, with one data set underestimating ChlA, and the other over-estimating ChlA (Figure 8). The RMS%E values for the two sets were found to be 64.2% and 212.3% respectively. Although the overall quality of the match-up was low, the underlying structure of the data suggests that the form of the relationship might be useful subject to appropriate optimization. Figure 8: Comparison of modelled vs. measured ChlA. ChlA values calculated using the [PERSON] et al. (2008) model and the [PERSON] et al. (2008) model are represented by dark grey squares and light grey diamonds respectively. The dashed grey line indicates the 1:1 relationship. Figure 7: **(a)** Comparison of modelled vs. measured POC. POC values calculated using the diatom model ([PERSON], 2000) are represented by dark grey squares; the RMS%E value refers to these. POC values calculated using the other three models are represented by light grey diamonds and triangles; **(b)** Cumulative distribution of modelled POC for the diatom model. Solid, dashed, and dotted lines represent median, upper/lower quartiles, and max./min. values respectively. The light grey horizontal lines mark the middle 90% of the contribution (i.e., from 5% to 95%) to the total POC value. The dashed grey line indicates the 1:1 relationship. When the refractive index-based \(C_{i}\) and \(Chl_{i}\) estimation models (Equations (4)-(7)) were applied to POC and ChIA modelling, the comparison between modelled and measured values of POC produced results (Figure 9a) which echo those found for SPM, ISM, and OSM when simple spherical particle volumes are used (see Figure 4). As was the case for particle mass values, the model POC values grossly overestimated the corresponding UKCW measurements, in certain cases by over two orders of magnitude. In contrast, the comparison between modelled and measured values of ChIA (Figure 9b) produced results which are similar to those found with the [PERSON] et al. [11] cell volume scaling model (see Figure 8): both the Stramski and the DuRand models i.e., Equations (5) and (7) underestimated the measured ChIA values, producing RMS%E values of 63.3% and 76.5% respectively. Following the successful application of a fractal model of particle volume to the modelling of SPM, ISM, and OSM values, the same fractal model was applied to the refractive index-based \(C_{i}\) and \(Chl_{i}\) estimation as well by simple substitution of the \(\rho\) term of Equation (10) with either \(C_{i}\) or \(Chl_{i}\). The POC values produced using the fractal procedure were found to model the corresponding UKCW measurements much better than those produced using the simple spherical model, with RMS%E values of 51.4% and 49.2% for the [PERSON] [19] and [PERSON] et al. [20] models respectively (Figure 9c).